The White House insisted Thursday that President Obama’s endorsement of Hillary Clinton, including gushing praise for her high “character,” won’t influence the Justice Department’s criminal investigation into her secret email system from her time as secretary of state.

Hours after he endorsed Mrs. Clinton for president and praised her for “making history” as the first female major-party nominee, Mr. Obama met privately in the Oval Office with Attorney General Loretta Lynch.

That meeting raised more questions about political pressure on federal prosecutors to go easy on Mrs. Clinton.

Donald Trump, the presumptive Republican presidential nominee, said Mr. Obama was backing “crooked Hillary” in bid for a third term of his policies. The chairman of the Republican National Committee, Reince Priebus, agreed that Mrs. Clinton is making history — as “the first-ever presidential candidate to be under an FBI investigation.”

White House press secretary Josh Earnest said Mr. Obama is “resolutely committed” to an independent investigation and he feels confident that FBI agents and other Justice officials won’t be influenced by the president’s support of Mrs. Clinton.

“They aren’t going to be swayed by political forces,” Mr. Earnest said. “They know that their investigation should be guided by the facts and that they should follow the evidence where it leads. The president has complete confidence that that’s exactly what they’ll do.”

He said the president has never discussed the Justice probe with Mrs. Clinton and that career Justice prosecutors treat the subjects of their investigations impartially “regardless of their political influence, regardless of their political party, regardless of their political stature and regardless of what political figure has endorsed them.”

The Justice probe of Mrs. Clinton’s private email server and release of classified government information remains the biggest hurdle for her candidacy as Democrats move to consolidate their support behind her.

Her rival for the Democratic nomination, Sen. Bernard Sanders of Vermont, met with Mr. Obama at the White House on Thursday morning and emerged sounding as if he is preparing to formally end his candidacy after the District of Columbia’s primary next week.

“I am going to do everything in my power, and I will work as hard as I can, to make sure that Donald Trump does not become president of the United States,” Mr. Sanders told reporters at the White House.

He said of Mrs. Clinton, “I look forward to meeting with her in the near future to see how we can work together to defeat Donald Trump and to create a government which represents all of us and not just the 1 percent.”

About 90 minutes later, Mr. Obama endorsed Mrs. Clinton in a video announcement on YouTube that was recorded Tuesday, around the time she was clinching the delegates needed for the nomination. Although the endorsement was hardly a surprise, it lent an air of confirmation about Mr. Sanders‘ plan to concede.

“I know how hard this job can be,” the president said. “That’s why I know Hillary will be so good at it. She’s got the courage, the compassion and the heart to get the job done. I have seen her judgment. I have seen her toughness. I’ve seen her commitment to our values up close.”

Mrs. Clinton welcomed the endorsement with a Twitter post: “Honored to have you with me, @POTUS. I’m fired up and ready to go!”

The post on the Clinton campaign Twitter account was signed “H,” which is supposed to indicate that Mrs. Clinton wrote the message herself.

The Clinton campaign quickly announced that Mr. Obama, whose job approval rating has been consistently above the key threshold of 50 percent this year, will make his first campaign appearance with Mrs. Clinton on Wednesday in Green Bay, Wisconsin.

“President Obama and Clinton will discuss building on the progress we’ve made and their vision for an America that is stronger together,” the campaign said in a statement.

The president, alarmed by Mr. Trump’s candidacy and believing the Republican isn’t fit to hold the office, has been eager to jump into the campaign fray on Mrs. Clinton’s behalf.

In his endorsement of Mrs. Clinton, the president said, “I don’t think there’s ever been someone so qualified to hold this office.”

The White House later amended that statement and said presidential candidates who served as vice president, such as Al Gore, could be considered as better qualified.

Mr. Earnest noted that Mrs. Clinton has served as secretary of state, as a U.S. senator and eight years as first lady, a post that allowed her to “travel the world.”

Mr. Trump was succinct in his reaction to the president’s endorsement. “Obama just endorsed Crooked Hillary,” the Republican said on Twitter. “He wants four more years of Obama — but nobody else does!”

Republican National Committee Chairman Reince Priebus said Mr. Obama’s endorsement shows that Mrs. Clinton “is running to give President Obama’s failed polices a third term.”

“President Obama has trampled the Constitution, buried our country in $9 trillion of crushing new debt, presided over the weakest economy in a generation and, with Clinton’s help, pursued a weak and dangerous foreign policy that has made us less safe, Mr. Priebus said.

He said Mrs. Clinton, while secretary of state, “put our national security at risk with her illicit email server, which she devised to skirt government transparency laws and obscure her unethical dealings as the nation’s top diplomat.”

“Hillary Clinton is the first-ever presidential candidate to be under an FBI investigation, and her corrupt family foundation that has taken millions from foreign governments is an unprecedented conflict of interest,” Mr. Priebus said. “I don’t think there’s been a candidate for this office more unethical and untrustworthy than Hillary Clinton.”

It’s unclear when Justice officials might conclude their investigation into Mrs. Clinton’s private email server, which Mr. Earnest referred to as a criminal probe.

Although Mr. Sanders will compete in the final primary next week, he said his campaign will focus on promoting statehood for the District of Columbia rather than his own candidacy.

The socialist said Mr. Trump would be “a disaster” as president.

“It is unbelievable to me, and I say this in all sincerity, that the Republican Party would have a candidate for president who in the year 2016 makes bigotry and discrimination the cornerstone of his campaign,” Mr. Sanders said. “In my view, the American people will not vote for or tolerate a candidate who insults Mexicans and Latinos, who insults Muslims, who insults African-Americans and women.”

Mr. Sanders drew huge crowds around the country in his upstart campaign and has given Mrs. Clinton an unexpectedly tough battle with his rhetoric accusing her of cozying up to Wall Street.

He didn’t say explicitly Thursday that he would concede and promised to keep pushing for more generous Social Security benefits, better health care, higher tuition aid and more spending on infrastructure.

“These are some of the issues that many millions of Americans have supported during my campaign,” he said. “These are the issues that we will take to the Democratic National Convention in Philadelphia at the end of July.”

He took no questions from reporters and walked away from shouted questions with his wife, Jane.

The Vermont independent’s meeting with the president lasted more than one hour. He praised Mr. Obama and Vice President Joseph R. Biden for “the degree of impartiality” in the Democratic primary.

“They said they would not put their thumb on the scales, and they kept their word,” Mr. Sanders said. “I appreciate that greatly.”

With some supporters urging Mr. Sanders to press on toward the Democratic National Convention next month, Mr. Obama had the delicate job of trying to show a clear end to the primary season so he and Mrs. Clinton could focus on campaigning against Mr. Trump.

But Mr. Obama doesn’t want to appear to be too heavy-handed with Mr. Sanders because Mrs. Clinton will need his millions of liberal supporters in the general election.

“My hope is, is that over the next couple of weeks, we’re able to pull things together,” Mr. Obama told “Tonight Show” host Jimmy Fallon in an interview that aired Thursday. “And what happens during primaries, you get a little ‘ouchy.’ Everybody does.”

He said the contested primary has been “a healthy thing for the Democratic Party.”

“I thought that Bernie Sanders brought enormous energy and new ideas,” the president said. “And he pushed the party and challenged them. I thought it made Hillary a better candidate.”

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