WASHINGTON — The federal prosecutor scrutinizing the Russia investigation has begun examining the role of the former C.I.A. director John O. Brennan in how the intelligence community assessed Russia’s 2016 election interference, according to three people briefed on the inquiry.

John H. Durham, the United States attorney leading the investigation, has requested Mr. Brennan’s emails, call logs and other documents from the C.I.A., according to a person briefed on his inquiry. He wants to learn what Mr. Brennan told other officials, including the former F.B.I. director James B. Comey, about his and the C.I.A.’s views of a notorious dossier of assertions about Russia and Trump associates.

Mr. Durham’s pursuit of Mr. Brennan’s records is certain to add to accusations that Mr. Trump is using the Justice Department to go after his perceived enemies. The president has long attacked Mr. Brennan as part of his narrative about a so-called deep state cabal of Obama administration officials who tried to sabotage his campaign, and Mr. Trump has held out Mr. Durham’s investigation as a potential avenue for proving those claims.

Mr. Durham is also examining whether Mr. Brennan privately contradicted his public comments, including May 2017 testimony to Congress, about both the dossier and about any debate among the intelligence agencies over their conclusions on Russia’s interference, the people said.