She dwelled on the historic nature of her achievement as the first woman at the top of a major party ticket, and even joked about the venue picked for her party — the glass encased Duggal Greenhouse in Brooklyn Navy Yard.

“Tonight’s victory is not about one person. It belongs to a generation of women and men who struggled and sacrificed and made this moment possible,” Clinton said.

NEW YORK — Hillary Clinton claimed her spot as the presumptive Democratic nominee for president in a speech Tuesday night that she’s been wanting to give for nearly a decade.

“It maybe be hard to see tonight but we are all standing under a glass ceiling right now,” Clinton said, referring the clear roofing. “But don’t worry, we’re not smashing this one, thanks to you — we’ve reached a milestone.”


In the last major round of voting in the primary election, Clinton padded her delegate lead with victories Tuesday in New Jersey, New Mexico, and South Dakota. Her rival Bernie Sanders landed a victory in North Dakota, a state with too few delegates to make a dent. Clinton led in early results from California, the big prize of the night, while Sanders led in Montana.

The crowd roared when Clinton came out to speak, even though many had waited at the venue for hours as the temperature increased along with the audience. She seemed to savor the moment — opening up both of her arms to welcome the cheers.

She congratulated Sanders, the Vermont senator, for running an “extraordinary campaign” and reached out to his millions of supporters.

“This has been a hard fought, deeply felt campaign,” Clinton said. “Now I know it never feels good to put your heart into a cause, or a candidate you believe in and to come up short. I know that feeling well,” she said, referring to her own loss eight years ago. “But as we look ahead to the battle that awaits let’s remember all that unites us.”


She spent much of the last half of her address slamming presumptive Republican nominee Donald Trump, who she said is “temperamentally unfit” to be president.

“He’s not just trying to build a wall between America and Mexico, he’s trying to wall off Americans,” she said.

Many held iPhones aloft to record the moment when she walked out on stage, and again at the end of her speech when Clinton was joined on stage by her visibly-pregnant daughter Chelsea, son-in-law Marc Mezvinsky, and her husband, former president Bill Clinton.

One person held up a sign that read “Caution: Shattered glass” — a reference to what she famously called to as “the highest, hardest glass ceiling” in her concession speech eight years ago to the day. Another group held up letters spelling “history.”

Clinton mathematically clinched the nomination Monday when a group of previously uncommitted superdelegates — party leaders who are not bound by primary votes — told the Associated Press they would back her.

President Obama spoke by the phone with both Clinton and Sanders Tuesday, according to the White House. He congratulated Clinton for her “historic campaign.’’

The White House said Sanders, at the Vermont senator’s request, would visit the president Thursday, a key step that could be a precursor to Sanders bowing out of the race. Sanders planned to lay off half his campaign staff on Wednesday, The New York Times reported.


In the phone call Tuesday, Obama “thanked Senator Sanders for energizing millions of Americans with his commitment to issues like fighting economic inequality and special interests’ influence on our politics,’’ the White House said.

Many of Clinton’s supporters said they came to her event Tuesday to witness history. Some sipped wine and beer in the balmy twilight outside her rally enjoying a commanding view of the Brooklyn Bridge in the background. Inside, sequined singers belted out pop tunes such as Katy Perry’s “Firework.”

“It’s about time . . . for a woman, and for Hillary,” said Jennifer Martin of Hollywood, Fla., who made the trip up to Brooklyn for the event.

Looking toward the general election contest, Martin said she’s nervous that Sanders’ supporters won’t fall into line behind Clinton.

“I have some concerns that their biases won’t let them see common sense,” Martin said.

Even as he made plans to meet the president and lay off much of his staff, Sanders signaled publicly during the day Tuesday that he’ll continue fighting for the nomination until all of the delegates meet in Philadelphia for the Democratic National Convention on July 25.

“They haven’t actually voted,” said Sanders’ campaign manager Jeff Weaver, who tried to cast the convention balloting as the final primary in the lengthy contest during a CNN interview Tuesday afternoon. “We have to wait and see what the superdelegates do.”

But privately a member of the Sanders team acknowledged in an interview with the Globe that the staff is in discussions with the Clinton campaign about next steps and unifying the party. Losses in California and other states would likely speed up those conversations, according to the aide, who was not authorized to discuss campaign strategy.


Though there’s no consensus within the Sanders campaign about what those next steps are, the Vermont senator plans to fly with top staff from California to Vermont on Wednesday and talks about what comes next for Sanders are expected to begin in earnest on the charter flight.

Should Sanders try to contest Clinton’s nomination past next Tuesday’s final primary in the District of Columbia, it’s unclear how much support he’ll continue to have even from the liberal outside groups who have cheered him from the start.

Democracy for America, a left-leaning group that endorsed Sanders early on, won’t help him change the minds of superdelegates.

“DFA believes that the winner of the majority of pledged delegates should be the Democratic nominee,” said Neil Sroka, a spokesman for the group.

And Democratic Party leaders, already supportive of Clinton, have been drawing even closer around her. Aides close to Obama signaled that he’s going to endorse Clinton in coming days.

Democratic House leader Nancy Pelosi stepped off the sidelines and declared her support for Clinton Tuesday morning.

“I’m a voter in California and I have voted for Hillary Clinton for president of the United States and proud to endorse her for that position,” she said in an interview on ABC’s “Good Morning America.”


Pelosi also threw a warm light on a notion that could help unify the party: A Democratic ticket that includes progressive champion Elizabeth Warren as vice president.

“We’ve had two men over and over again for hundreds of years,” said Pelosi, when asked about Warren. “I think that two women, whoever they may be, that would be fabulous.”

Warren, the Massachusetts senator, hasn’t endorsed in the contest — but has used her social media accounts to focus on attacking Trump.

Clinton’s team asked surrogates Tuesday to use Trump as a motivator for party unity.

“Donald Trump poses too big of a threat for us to become complacent — we need to finish strong so we’re ready to take him on full steam ahead,” according to a Clinton campaign memo distributed to her supporters.

She’s also focusing her schedule on the general election with trips set for swing states.

When the residents of the District of Columbia cast ballots in the final primary contest next Tuesday, Clinton plans to be in Pennsylvania campaigning against Trump.

Results from Tuesday’s primaries:

New Jersey

New Mexico

North Dakota

South Dakota

California

Montana

Annie Linskey can be reached at annie.linskey@globe.com. Follow her on Twitter @annielinskey. Victoria McGrane can be reached at victoria.mcgrane@globe.com. Follow her on Twitter @vgmac.