The White House broke with Democrats on Monday, saying FBI Director James B. Comey was “a man of integrity” and shooting down accusations that he is intentionally meddling with the election to try to stop Hillary Clinton from becoming president.

Press secretary Josh Earnest said Mr. Comey didn’t divulge many details, so it’s difficult to either criticize or defend the top cop. But the spokesman undercut the claims of those such as Senate Minority Leader Harry Reid, Nevada Democrat, who accused Mr. Comey of breaking the law by revealing that he has renewed his probe into Mrs. Clinton’s secret emails from her time in the State Department.

“The president doesn’t believe that Director Comey is intentionally trying to influence the outcome of an election. The president doesn’t believe that he’s secretly strategizing to benefit one candidate or one political party.”

Donald Trump gloated over the chaos within Democratic circles and said “it took guts” for Mr. Comey to buck political pressure. Speaking on the campaign trail, the Republican presidential nominee urged Mr. Comey to “hang tough.”

Mrs. Clinton’s team, meanwhile, shifted tactics and said the FBI must now reveal whether it is investigating Mr. Trump’s associates for illicit connections to Russia.

“It’s impossible to view this as anything less than a blatant double standard,” Clinton campaign manager Robby Mook told reporters on a conference call Monday afternoon.

The FBI has obtained a warrant to go through messages found on a device belonging to Mrs. Clinton’s close personal aide Huma Abedin and her estranged husband, former Rep. Anthony D. Weiner. Mr. Comey, in a letter to Congress last week, said the messages may be “pertinent” to the investigation into Mrs. Clinton’s mishandling of classified emails.

But Mr. Comey didn’t say any more than that, leaving all sides to draw their own conclusions. Republicans said the announcement meant Mrs. Clinton was once again in legal jeopardy. Democrats said Mr. Comey was too vague to draw any inferences and that Mrs. Clinton will be cleared once again.

In a letter to members of Congress who complained last week about the timing, Assistant Attorney General Peter J. Kadzik said the FBI was working “as expeditiously as possible.” But he didn’t provide any new details.

With just a week to go before the election and polls tightening, the Clinton campaign and its allies ramped up attacks on Mr. Comey and Mr. Trump.

Their newest line of fire was leveled against former Trump campaign manager Paul Manafort, whom Democrats have demanded be investigated after press reports this summer detailed his work on behalf of pro-Russian entities.

“If it comes out after the election that the FBI kept secret from the American people the fact that it was investigating former Trump campaign manager Paul Manafort, or seeking access to his emails, or investigating anyone else associated with Trump, then I have no idea how Director Comey will be able to explain his actions,” said Rep. Elijah E. Cummings of Maryland, the ranking Democrat on the House Oversight and Government Reform Committee.

Mr. Comey refused to comment earlier this year when asked in congressional hearings whether he was probing Mr. Trump or his associates. He said such a disclosure would be inappropriate.

But the Clinton campaign said that explanation must now fall.

“Director Comey is the one who opened this door. He is the one who started breaking protocol and commenting on investigations before they were concluded,” Mr. Mook said.

The Clinton campaign said Mr. Comey just weeks ago appeared to abide by the pre-election rule when, according to a CNBC report, he refused to join a communique blaming Russia for email hacks against Democrats. They wondered why he acted differently when it came to the Clinton emails.

Mr. Comey has been second-guessed by former Justice Department officials who served in both Democratic and Republican administrations.

While the White House didn’t criticize Mr. Comey’s actions or defend him, Mr. Earnest repeatedly pointed out that the president believes the Justice Department should “limit public discussion” of ongoing investigations. He said the “long-standing” principle should apply “even when we’re not talking about someone famous, and even when we’re not talking about an election being a week and a half away.”

“The president believes that he is a man of integrity, he’s a man of character, he’s a man of principle and he’s got a very difficult job,” Mr. Earnest said. “And those character traits that I just described will serve him well as he works through the difficult challenges that he faces over the course of his job.”

Mr. Comey closed out his investigation into Mrs. Clinton’s emails in July, ruling that while she did mishandle top-secret information, she was too technologically inept and had too little understanding of classified information for prosecutors to prove that she intended to break secrecy laws.

It’s not clear what the newly uncovered emails have to do with that investigation — which is why Democrats say Mr. Comey owes the public more information.

A Republican who oversees the FBI, Senate Judiciary Committee Chairman Chuck Grassley of Iowa, agreed that Mr. Comey must say more. He asked for a complete rundown of the emails that agents say they have uncovered.

“In the absence of additional, authoritative information from the FBI in the wake of your vague disclosure, Congress and the American people are left to sift through anonymous leaks from Justice Department officials to the press of varying levels of detail, reliability and consistency,” Mr. Grassley said. “The American people deserve better than that.”

But Mr. Grassley also asked Mr. Comey to promise his investigation won’t be hamstrung by strict limits. In the yearlong probe that ended in July, the FBI and Justice Department prosecutors offered immunity to several witnesses and struck side agreements limiting how they would obtain and use some of the email evidence in the case.

⦁ Stephen Dinan contributed to this report.

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