President Trump made clear this week that Tulsi Gabbard was back in his good graces.

A few weeks ago, Mr. Trump excoriated Ms. Gabbard, one of his top intelligence officials, over a video she filmed during a trip to Asia that he saw as self-promotional, and she was left out of some meetings in the lead-up to the U.S. strikes on Iranian nuclear facilities, according to two people with knowledge of what happened.

But on Tuesday, at a White House event with congressional Republicans that Ms. Gabbard attended, he declared: “She’s, like, hotter than everybody. She’s the hottest one in the room right now.”

What changed? Last week, Ms. Gabbard launched a diversionary attack that relieved pressure on Mr. Trump from the never-ending Epstein file crisis, releasing documents, she claimed, that proved Obama administration officials engaged in a “treasonous conspiracy.”

Yet Ms. Gabbard’s effort to repair her standing with the president has placed the already embattled Attorney General Pam Bondi in a nearly untenable position.

Ms. Bondi was given little warning the director of national intelligence was about to demand she investigate one of Mr. Trump’s most longstanding grievances: claims without evidence that the Obama administration overstated Russia’s meddling in the 2016 election in order to undermine him.

Ms. Bondi, fresh off a nasty fight with a top F.B.I. official over who was responsible for the political mess around the Epstein case, felt blindsided and annoyed, according to several people familiar with her thinking. They said that in reality, however, Ms. Gabbard was acting as little more than a proxy for a president demanding action on his vengeance agenda.

Ms. Bondi’s staff scrambled for a solution that would satisfy Mr. Trump while not committing the department to a tit-for-tat Obama investigation with unpredictable legal and political consequences.

Ms. Gabbard, standing at the White House briefing room lectern on Wednesday, made a series of provocative claims and pointedly said the onus was now on the Justice Department.

Several hours later, Ms. Bondi’s deputies posted an ambiguous, four-paragraph statement on the department’s website that announced the formation of what they described as a “strike force” to look into the Gabbard accusations. In a rare direct engagement with the Trump administration, a spokesman for former President Barack Obama dismissed the attacks as a “ridiculous and a weak attempt at distraction.”

Further details of the group’s operations, timetable and composition were not forthcoming. Officials close to the situation said the details were being hammered out. A similar effort set up to address “weaponization” of the Biden-era Justice Department has yet to yield much.

Representatives of Ms. Gabbard and Ms. Bondi deny there is any friction, insisting they are in lock step.

“Director Gabbard and Attorney General Bondi have been in frequent contact and are working together to hold those responsible for manufacturing the Russia hoax accountable,” said Olivia Coleman, a spokeswoman for Ms. Gabbard.

The attorney general described Ms. Gabbard as “a friend” and said in a statement that she was “grateful for her partnership.”

It is not guaranteed that the move will satisfy Mr. Trump, who has repeatedly demanded the Justice Department investigate and prosecute political enemies and those responsible for bringing state and federal charges against him.

Mr. Trump has recently told advisers that he fully supports Ms. Bondi and values her loyalty, though he has complained that senior department officials, including Ms. Bondi, were not moving fast enough to investigate those he has labeled criminals, including Mr. Obama, according to multiple people in the president’s orbit.

Harrison Fields, a White House spokesman, said Mr. Trump was “incredibly happy” with both Ms. Bondi and Ms. Gabbard, but signaled the White House was eager to see the Justice Department use the information from the Office of the Director of National Intelligence.

Ms. Gabbard “has outlined a credible case that pursues the president’s goal of transparency and accountability, and now it resides in the Department of Justice, where the president has full confidence in her ability to do a full investigation and come up with findings based on the information provided to her,” Mr. Fields said.

Current and former officials said that building a coherent conspiracy case against former intelligence officials that can withstand the scrutiny of appeals court judges would be challenging. A case against Mr. Obama himself would be practically impossible.

The immunity ruling by the Supreme Court last year, three of whose members were picked by Mr. Trump, has made it difficult to prosecute former presidents for official acts.

But that has not stopped Ms. Gabbard.

“The evidence that we have found and that we have released directly point to President Obama leading the manufacturing of this intelligence assessment,” she said on Wednesday, though she produced no evidence of wrongdoing on Mr. Obama’s part. “There are multiple pieces of evidence and intelligence that confirm that fact.”

Former officials said Ms. Gabbard, by accusing Mr. Obama of wrongdoing, stepped outside the boundaries meant to contain intelligence officials. Making accusations of criminal wrongdoing is the job of prosecutors, not spy agencies, they said.

Two Republican senators, Lindsey Graham of South Carolina and John Cornyn of Texas, offered Ms. Bondi a way out of the bind on Thursday, calling on her to outsource the matter to a special counsel. Doing so would require a tactical U-turn: She has opposed the use of special counsels in political cases.

Yet securing convictions might be beside the point.

Mr. Trump has kept up a steady bombardment of suggestions, requests and demands to arrest, investigate or prosecute targets of his choosing: the former F.B.I. director James B. Comey, various Democrats, prosecutors who investigated him, officials who rejected his election lies, Beyoncé, Bruce Springsteen, former President Joseph R. Biden Jr.

Part of his motivation, people around Mr. Trump have long said, is to humiliate his enemies.

“After what they did to me, and whether it’s right or wrong, it’s time to go after people,” Mr. Trump said on Tuesday of his desired Obama prosecution.

Earlier this year, Ed Martin, a Trump loyalist and the self-described “captain” of the Justice Department’s “weaponization” group, said he planned to use his authority to expose and discredit those he believes to be guilty, even if he cannot find sufficient evidence to prosecute them — weaponizing an institution he has been hired to de-weaponize, in the view of critics.

“If they can be charged, we’ll charge them,” Mr. Martin told reporters earlier this year. “But if they can’t be charged, we will name them.”

Ms. Gabbard has raised expectations beyond anything the Justice Department could likely meet without potentially inviting a judicial rebuke or prompting a political backlash for attacking Mr. Obama, a still-formidable political figure who enjoys widespread respect.

Ms. Gabbard’s talk of treasonous conspiracy and suggestion that Mr. Obama wanted to undermine his successor have played well with Mr. Trump. This week he connected the conspiracy from the 2016 intelligence assessment to the 2020 election, which he falsely insisted was rigged.

“We’re very proud of you, Tulsi,” Mr. Trump said Tuesday at the gathering with congressional Republicans. “They cheated so badly, and ultimately it led to loss in 2020, and it shouldn’t have been a loss. It was a big victory. We won by a lot.”

For any conspiracy charge to pass legal muster, it must be for an act that falls within the statute of limitations, meaning it would have to extend beyond the Obama administration into Mr. Trump’s first term or the Biden administration.

Ms. Gabbard was asked on Wednesday about the statute of limitations applying to conspiracy charges.

“It’s a great question for Attorney General Pam Bondi,” she said. “We’re providing all of the evidence, all of the intelligence that we have, both redacted and unredacted versions.”

Ms. Gabbard’s documents have also not presented evidence of a conspiracy against Mr. Trump or undermined the central contention that Russia attempted to influence the 2016 election.

A report she issued last week was critical of pressure from Mr. Obama and top officials to complete the intelligence assessment before leaving office. But top officials asking a government agency to work faster is hardly criminal.

That report also conflated two different ideas: assessments about efforts by Russia to hack voting infrastructure and to leak information damaging to Hillary Clinton, the Democratic presidential candidate in 2016. By conflating the two questions, the report incorrectly suggested that the spy agencies, under pressure from senior officials, had changed their view about whether Russia meddled in the election.

Nothing Ms. Gabbard said on Wednesday undermined the findings that Russia attempted to meddle in the election. But she leaned into the idea of conspiracy nevertheless, accusing former officials of suppressing evidence and ignoring standards.

“In doing so,” she said, “they conspired to subvert the will of the American people who elected Donald Trump in that election in November of 2016.”

Maggie Haberman contributed reporting.