Pursuing a theory promoted by Trump loyalists, the Justice Department is investigating whether F.B.I. officials during and after the Biden administration tried to hide or secretly destroy documents that might cast doubt on the earlier inquiry into Russia’s attempt to tilt the 2016 election in President Trump’s favor, two people with knowledge of the matter said.

The steps taken by the Justice Department are the latest in a series of efforts by Mr. Trump and his allies to impugn the Russia investigation, which the president sees as having been a partisan witch hunt that unfairly dogged him throughout his first term.

The new inquiry seeks to determine if senior F.B.I. officials spent years working to cover up the supposed misdeeds of James B. Comey, the F.B.I. director at the time of the Russia investigation, and John O. Brennan, who was then the C.I.A. director, after the two men left government by squirreling away potentially damaging classified documents.

The disclosures bring into sharper focus how Kash Patel, now the F.B.I. director, is intent on substantiating longstanding claims Mr. Trump has peddled to his base that he was framed by the Obama administration. Under Mr. Patel and his deputy, Dan Bongino, the bureau has moved to oust employees they believe are disloyal or who have worked on investigations into Mr. Trump.

The investigation is examining the conduct of the bureau’s former deputy director, Paul Abbate, a veteran agent who served in the role throughout the Biden administration and stepped down on Jan. 20, the day Mr. Trump was sworn into office, the people with knowledge of the matter said. Investigators are also examining conduct by other senior F.B.I. officials in the bureau’s headquarters this year, they said.

One person familiar with the investigation said that prosecutors and agents appeared to be investigating claims in an article published in July by Fox News that said thousands of pages of documents related to the Russia investigation had been found in burn bags at the F.B.I.