(CNN) Hillary Clinton embraced her moment in history Tuesday, becoming the first woman in the 240-year life of the United States to lead the presidential ticket of a major political party.

"Thanks to you, we've reached a milestone," she said during a speech in Brooklyn. "Tonight's victory is not about one person. It belongs to generations of women and men who struggled and sacrificed and made this moment possible."

After three decades at the center of American politics as a pioneering -- and deeply controversial -- feminist icon, the victory brings Clinton, 68, within reach of finally cracking the "highest, hardest glass ceiling" she lamented eight years ago when she conceded the Democratic race to Barack Obama. The former first lady, senator from New York and secretary of state will now face presumptive Republican nominee Donald Trump in a general election battle that is already shaping up as one of the nastiest campaigns in modern U.S. history.

Clinton has pounced on Trump's business record, character and tendency to use his platform to wage personal grudge matches to try to define him early on in the minds of voters as unfit for the presidency. Trump, for his part, is aiming to portray Clinton as a consistent liar who can't be trusted.

Though Clinton already has Trump in her sights, she has work to do to unify her own party after a grueling battle against Bernie Sanders. The Vermont senator spoke before a roaring crowd of his own in California to declare "the struggle continues." The Vermont senator pledged to stay in the race through next week's primary in Washington, D.C., and to fight on for social, economic, racial and environmental justice at the Democratic National Convention in Philadelphia.

Obama's call

President Barack Obama, who waited until voting ended in the last six primary states to weigh in on the race, called both candidates to congratulate them for "running inspiring campaigns that have energized Democrats," according to a White House statement.

But the President, who will meet with Sanders Thursday at the Vermont senator's request, clearly sided with Clinton by lauding her for "securing the delegates necessary to clinch the Democratic nomination for President."

Photos: Female firsts in politics Hillary Clinton, a former first lady, U.S. senator and secretary of state, claims her place in history on Tuesday, July 27, after becoming the Democratic Party's nominee for U.S. President. She would be the first woman in U.S. history to lead the ticket of a major political party. Hide Caption 1 of 16 Photos: Female firsts in politics Elizabeth Cady Stanton was the first woman to run for a seat in the U.S. House of Representatives. She was a leader of the suffragette movement along with Lucretia Mott and Susan B. Anthony. She was also the editor of the feminist magazine "Revolution." Hide Caption 2 of 16 Photos: Female firsts in politics In 1916, Jeannette Rankin was the first woman to be elected to the U.S. House of Representatives. The Republican from Montana was the only member of Congress to vote against U.S. entry in both World War I and World War II. Hide Caption 3 of 16 Photos: Female firsts in politics Feminist reformer Victoria Claflin Woodhull was the first woman to run for U.S. President from a nationally recognized ticket. She was the candidate of the Equal Rights Party in 1872. Hide Caption 4 of 16 Photos: Female firsts in politics Frances Perkins was the first woman to serve as a member of the President's Cabinet. She was appointed labor secretary by President Franklin D. Roosevelt in 1933. Hide Caption 5 of 16 Photos: Female firsts in politics Shirley Chisholm, a Democrat from New York, was the first African-American woman to be elected to the U.S. House of Representatives. She was elected in 1968. Hide Caption 6 of 16 Photos: Female firsts in politics Sandra Day O'Connor was the first woman to be appointed to the U.S. Supreme Court. She was appointed by President Ronald Reagan in 1981. Hide Caption 7 of 16 Photos: Female firsts in politics In 1984, Geraldine Ferraro became the first woman to run on a major party's national ticket. She was Walter Mondale's running mate. Hide Caption 8 of 16 Photos: Female firsts in politics U.S. Rep. Ileana Ros-Lehtinen, a Republican from Florida, was elected in 1989. She is the first Hispanic woman and Cuban-American to be elected to the U.S. House of Representatives. Hide Caption 9 of 16 Photos: Female firsts in politics Carol Moseley Braun, a Democrat from Illinois, was the first African-American woman to be elected to the U.S. Senate. She served from 1993 to 1999. Hide Caption 10 of 16 Photos: Female firsts in politics Dee Dee Myers was the first woman to serve as White House press secretary. She was appointed by President Bill Clinton and held the position from January 1993 to December 1994. Hide Caption 11 of 16 Photos: Female firsts in politics Madeleine Albright was the first woman to serve as U.S. secretary of state. She was appointed to the position by President Bill Clinton in 1997. Hide Caption 12 of 16 Photos: Female firsts in politics U.S. Sen. Tammy Baldwin, a Democrat from Wisconsin, is the first openly gay woman to be elected to Congress. She was elected to the House in 1999 and to the Senate in 2012. Hide Caption 13 of 16 Photos: Female firsts in politics House Minority Leader Nancy Pelosi, a Democrat from California, is the first woman to lead a party in Congress. Hide Caption 14 of 16 Photos: Female firsts in politics Sonia Sotomayor is the first Hispanic woman to serve on the Supreme Court. She was nominated by President Barack Obama in 2009. Hide Caption 15 of 16 Photos: Female firsts in politics U.S. Sen. Mazie Hirono, a Democrat from Hawaii, is the first woman of color to serve in both chambers of Congress. Hirono was elected to the House in 2007 and to the Senate in 2012. Hide Caption 16 of 16

"Her historic campaign inspired millions and is an extension of her lifelong fight for middle-class families and children," the statement said.

Reaching the highest peak yet in a tumultuous and trailblazing political career, Clinton claimed victory exactly eight years after folding her 2008 Democratic primary campaign against Obama.

Her long-awaited moment of celebration came as she notched wins in the night's primaries in California, New Jersey, South Dakota and New Mexico Democratic primaries, according to CNN projections.

Clinton took the stage in Brooklyn to an explosion of cheers from her crowd, in the kind of eruption of enthusiasm that has been fleeting during much of her campaign. Clearly delighted, she stood with her arms outstretched on stage, savoring the adulation.

Reaching out to Sanders supporters, Clinton praised the Vermont senator for his long public service and mirrored some of his progressive economic rhetoric. She played down any notion of divisions and said their vigorous primary campaign was "very good for the Democratic Party and for America."

But in a sign of the task she faces in uniting the party, Sanders supporters loudly booed her name when he said he had received a "gracious" call from his rival and said he had congratulated her on her victories on Tuesday.

Sanders confounded the notion that the end of the state primary races would mean the end of his campaign.

"Next Tuesday, we continue the fight in the last primary in Washington DC," Sanders said. "We are going to fight hard to win the primary in Washington, D.C., and then we take our fight for social, economic, racial and environmental justice to Philadelphia."

"I am pretty good at arithmetic and I know that the fight in front of us in a very, very steep fight."

But Sanders vowed to fight on for every delegate and every vote.

Clinton vs. Trump

While Sanders signaled that he was not yet ready to fold a campaign that started with him as a fringe candidate and ignited a startling grass roots uprising that won more than 10 million votes, Clinton looked ahead to the general election.

Clinton intensified her assault on Trump, laying out a case that his values and rhetoric are incompatible with American principles and that he's "temperamentally unfit" to be President.

"He is not just trying to build a wall between America and Mexico. He is trying to wall of Americans from each other. When he says let's make America great again, that is code for let's take American backwards."

She hit Trump hard for his recent attacks on a judge with Mexican ancestry along with mocking a disabled reporter and calling "women pigs."

Photos: Hillary Clinton's life in the spotlight Photos: Hillary Clinton's life in the spotlight Hillary Clinton accepts the Democratic Party's nomination for president at the Democratic National Convention in Philadelphia on July 28, 2016. The former first lady, U.S. senator and secretary of state was the first woman to lead the presidential ticket of a major political party. Hide Caption 1 of 43 Photos: Hillary Clinton's life in the spotlight Before marrying Bill Clinton, she was Hillary Rodham. Here she attends Wellesley College in Massachusetts. Her commencement speech at Wellesley's graduation ceremony in 1969 attracted national attention. After graduating, she attended Yale Law School. Hide Caption 2 of 43 Photos: Hillary Clinton's life in the spotlight Rodham was a lawyer on the House Judiciary Committee, whose work led to impeachment charges against President Richard Nixon in 1974. Hide Caption 3 of 43 Photos: Hillary Clinton's life in the spotlight In 1975, Rodham married Bill Clinton, whom she met at Yale Law School. He became the governor of Arkansas in 1978. In 1980, the couple had a daughter, Chelsea. Hide Caption 4 of 43 Photos: Hillary Clinton's life in the spotlight Arkansas' first lady, now using the name Hillary Rodham Clinton, wears her inaugural ball gown in 1985. Hide Caption 5 of 43 Photos: Hillary Clinton's life in the spotlight The Clintons celebrate Bill's inauguration in Little Rock, Arkansas, in 1991. He was governor from 1983 to 1992, when he was elected President. Hide Caption 6 of 43 Photos: Hillary Clinton's life in the spotlight Bill Clinton comforts his wife on the set of "60 Minutes" after a stage light broke loose from the ceiling and knocked her down in January 1992. Hide Caption 7 of 43 Photos: Hillary Clinton's life in the spotlight In June 1992, Clinton uses a sewing machine designed to eliminate back and wrist strain. She had just given a speech at a convention of the International Ladies' Garment Workers Union. Hide Caption 8 of 43 Photos: Hillary Clinton's life in the spotlight During the 1992 presidential campaign, Clinton jokes with her husband's running mate, Al Gore, and Gore's wife, Tipper, aboard a campaign bus. Hide Caption 9 of 43 Photos: Hillary Clinton's life in the spotlight Clinton accompanies her husband as he takes the oath of office in January 1993. Hide Caption 10 of 43 Photos: Hillary Clinton's life in the spotlight The Clintons share a laugh on Capitol Hill in 1993. Hide Caption 11 of 43 Photos: Hillary Clinton's life in the spotlight Clinton unveils the renovated Blue Room of the White House in 1995. Hide Caption 12 of 43 Photos: Hillary Clinton's life in the spotlight Clinton waves to the media in January 1996 as she arrives for an appearance before a grand jury in Washington. The first lady was subpoenaed to testify as a witness in the investigation of the Whitewater land deal in Arkansas. The Clintons' business investment was investigated, but ultimately they were cleared of any wrongdoing. Hide Caption 13 of 43 Photos: Hillary Clinton's life in the spotlight The Clintons hug as Bill is sworn in for a second term as President. Hide Caption 14 of 43 Photos: Hillary Clinton's life in the spotlight The first lady holds up a Grammy Award, which she won for her audiobook "It Takes a Village" in 1997. Hide Caption 15 of 43 Photos: Hillary Clinton's life in the spotlight The Clintons dance on a beach in the U.S. Virgin Islands in January 1998. Later that month, Bill Clinton was accused of having a sexual relationship with former White House intern Monica Lewinsky. Hide Caption 16 of 43 Photos: Hillary Clinton's life in the spotlight Clinton looks on as her husband discusses the Monica Lewinsky scandal in the Roosevelt Room of the White House on January 26, 1998. Clinton declared, "I did not have sexual relations with that woman." In August of that year, Clinton testified before a grand jury and admitted to having "inappropriate intimate contact" with Lewinsky, but he said it did not constitute sexual relations because they had not had intercourse. He was impeached in December on charges of perjury and obstruction of justice. Hide Caption 17 of 43 Photos: Hillary Clinton's life in the spotlight The first family walks with their dog, Buddy, as they leave the White House for a vacation in August 1998. Hide Caption 18 of 43 Photos: Hillary Clinton's life in the spotlight President Clinton makes a statement at the White House in December 1998, thanking members of Congress who voted against his impeachment. The Senate trial ended with an acquittal in February 1999. Hide Caption 19 of 43 Photos: Hillary Clinton's life in the spotlight Clinton announces in February 2000 that she will seek the U.S. Senate seat in New York. She was elected later that year. Hide Caption 20 of 43 Photos: Hillary Clinton's life in the spotlight Clinton makes her first appearance on the Senate Environment and Natural Resources Committee. Hide Caption 21 of 43 Photos: Hillary Clinton's life in the spotlight Sen. Clinton comforts Maren Sarkarat, a woman who lost her husband in the September 11 terrorist attacks, during a ground-zero memorial in October 2001. Hide Caption 22 of 43 Photos: Hillary Clinton's life in the spotlight Clinton holds up her book "Living History" before a signing in Auburn Hills, Michigan, in 2003. Hide Caption 23 of 43 Photos: Hillary Clinton's life in the spotlight Clinton and another presidential hopeful, U.S. Sen. Barack Obama, applaud at the start of a Democratic debate in 2007. Hide Caption 24 of 43 Photos: Hillary Clinton's life in the spotlight Obama and Clinton talk on the plane on their way to a rally in Unity, New Hampshire, in June 2008. She had recently ended her presidential campaign and endorsed Obama. Hide Caption 25 of 43 Photos: Hillary Clinton's life in the spotlight Obama is flanked by Clinton and Vice President-elect Joe Biden at a news conference in Chicago in December 2008. He had designated Clinton to be his secretary of state. Hide Caption 26 of 43 Photos: Hillary Clinton's life in the spotlight Clinton, as secretary of state, greets Russian Prime Minister Vladimir Putin during a meeting just outside Moscow in March 2010. Hide Caption 27 of 43 Photos: Hillary Clinton's life in the spotlight The Clintons pose on the day of Chelsea's wedding to Marc Mezvinsky in July 2010. Hide Caption 28 of 43 Photos: Hillary Clinton's life in the spotlight In this photo provided by the White House, Obama, Clinton, Biden and other members of the national security team receive an update on the mission against Osama bin Laden in May 2011. Hide Caption 29 of 43 Photos: Hillary Clinton's life in the spotlight Clinton checks her Blackberry inside a military plane after leaving Malta in October 2011. In 2015, The New York Times reported that Clinton exclusively used a personal email account during her time as secretary of state. The account, fed through its own server, raises security and preservation concerns. Clinton later said she used a private domain out of "convenience," but admits in retrospect "it would have been better" to use multiple emails. Hide Caption 30 of 43 Photos: Hillary Clinton's life in the spotlight Clinton arrives for a group photo before a forum with the Gulf Cooperation Council in March 2012. The forum was held in Riyadh, Saudi Arabia. Hide Caption 31 of 43 Photos: Hillary Clinton's life in the spotlight Obama and Clinton bow during the transfer-of-remains ceremony marking the return of four Americans, including U.S. Ambassador Christopher Stevens, who were killed in Benghazi, Libya, in September 2012. Hide Caption 32 of 43 Photos: Hillary Clinton's life in the spotlight Clinton ducks after a woman threw a shoe at her while she was delivering remarks at a recycling trade conference in Las Vegas in 2014. Hide Caption 33 of 43 Photos: Hillary Clinton's life in the spotlight Clinton, now running for President again, performs with Jimmy Fallon during a "Tonight Show" skit in September 2015. Hide Caption 34 of 43 Photos: Hillary Clinton's life in the spotlight Clinton testifies about the Benghazi attack during a House committee meeting in October 2015. "I would imagine I have thought more about what happened than all of you put together," she said during the 11-hour hearing. "I have lost more sleep than all of you put together. I have been wracking my brain about what more could have been done or should have been done." Months earlier, Clinton had acknowledged a "systemic breakdown" as cited by an Accountability Review Board, and she said that her department was taking additional steps to increase security at U.S. diplomatic facilities. Hide Caption 35 of 43 Photos: Hillary Clinton's life in the spotlight U.S. Sen. Bernie Sanders shares a lighthearted moment with Clinton during a Democratic presidential debate in October 2015. It came after Sanders gave his take on the Clinton email scandal. "The American people are sick and tired of hearing about the damn emails," Sanders said. "Enough of the emails. Let's talk about the real issues facing the United States of America." Hide Caption 36 of 43 Photos: Hillary Clinton's life in the spotlight Clinton is reflected in a teleprompter during a campaign rally in Alexandria, Virginia, in October 2015. Hide Caption 37 of 43 Photos: Hillary Clinton's life in the spotlight Clinton walks on her stage with her family after winning the New York primary in April. Hide Caption 38 of 43 Photos: Hillary Clinton's life in the spotlight After Clinton became the Democratic Party's presumptive nominee, this photo was posted to her official Twitter account. "To every little girl who dreams big: Yes, you can be anything you want -- even president," Clinton said. "Tonight is for you." Hide Caption 39 of 43 Photos: Hillary Clinton's life in the spotlight Obama hugs Clinton after he gave a speech at the Democratic National Convention in Philadelphia. The president said Clinton was ready to be commander in chief. "For four years, I had a front-row seat to her intelligence, her judgment and her discipline," he said, referring to her stint as his secretary of state. Hide Caption 40 of 43 Photos: Hillary Clinton's life in the spotlight Clinton arrives at a 9/11 commemoration ceremony in New York on September 11. Clinton, who was diagnosed with pneumonia two days before, left early after feeling ill. A video appeared to show her stumble as Secret Service agents helped her into a van. Hide Caption 41 of 43 Photos: Hillary Clinton's life in the spotlight Clinton addresses a campaign rally in Cleveland on November 6, two days before Election Day. She went on to lose Ohio -- and the election -- to her Republican opponent, Donald Trump. Hide Caption 42 of 43 Photos: Hillary Clinton's life in the spotlight After conceding the presidency to Trump in a phone call earlier, Clinton addresses supporters and campaign workers in New York on Wednesday, November 9. Her defeat marked a stunning end to a campaign that appeared poised to make her the first woman elected US president. Hide Caption 43 of 43

"He wants to win by stoking fear and rubbing salt in wounds and reminding us daily just how great he is."

Clinton also signaled a robust challenge to Trump resonating with gender and personal themes. She spoke of how her late mother, Dorothy Rodham, taught her "never to back down from a bully."

Sanders faces an existential campaign question. He is grappling with whether to honor his vow to fight on to the Democratic National Convention next month or accept the electoral mathematics that give him no viable path to victory and join Clinton to unite a party divided by a much more competitive primary race than expected.

CNN's Brianna Keilar reported that the campaign managers for Clinton and Sanders are in touch, keeping the lines of communication open so they can eventually unify the party, according to a source familiar with the conversations.

The New York Times reported the Sanders campaign is about to undergo a significant reduction in staff. A top campaign official would neither confirm nor deny the report to CNN. But notably, as the campaign reaches the end of the primary season, the campaign has not moved to staff key battleground states and little appears in the works beyond recent promises to fight to the convention.

Trump's controversy

For Trump, the question Tuesday was how he would extricate himself from the political hole opened up by his controversial comments about a judge of Mexican descent who is overseeing a lawsuit aimed at Trump University. His accusation that the judge is biased because of his ethnicity has horrified senior GOP leaders who recently reluctantly endorsed him. He tried to neutralize the furor with a statement Tuesday saying his comments had been "misconstrued."

Amid the furor, Trump, who won the Republican contests Tuesday, delivered a more conventional speech that seemed a departure from the free wheeling approach he often takes. Using a teleprompter -- notable for someone who has blasted Clinton for being scripted -- Trump attacked Clinton and called for GOP unity. For one night at least, it seemed that the unpredictable billionaire had heeded calls by the GOP establishment -- which he built a campaign on vilifying -- to rein himself in for the good of the party.

"We are only getting started and it is going to be beautiful," he said.

He didn't mention the judge during his speech and instead sought to convey that he understood his new role as the leader of the GOP.

"I understand the responsibility of carrying the mantle and I will never, ever let you down," he said.

A top campaign adviser told CNN's Jim Acosta that Trump's speech was "very important to recovering from these five bad days."