The F.B.I. did not use information from the C.I.A. in opening the Russia investigation, former American officials said. But agents’ views on Russia’s election interference operation crystallized by mid-August, after the C.I.A. director at the time, John O. Brennan, shared intelligence with Mr. Comey about it.

The C.I.A. did contribute heavily to the intelligence community’s assessment in early 2017 that Russia interfered in the 2016 election and tried to tip it in Mr. Trump’s favor, and law enforcement officials later used those findings to bolster their application for a wiretap on a Trump campaign adviser, Carter Page.

The special counsel who took over the Russia investigation in 2017, Robert S. Mueller III, secured convictions or guilty pleas from a handful of Trump associates and indictments of more than two dozen Russians on charges related to their wide-ranging interference scheme.

In his report, Mr. Mueller said that he had “insufficient evidence” to determine whether Mr. Trump or his aides engaged in a criminal conspiracy with the Russians but that the campaign welcomed the sabotage and expected to benefit from it.

Mr. Barr is closely managing the Durham investigation, even traveling to Italy to seek help from officials there to run down an unfounded conspiracy that is at the heart of conservatives’ attacks on the Russia investigation — that the Italian government helped set up the Trump campaign adviser who was told in 2016 that the Russians had damaging information that could hurt Clinton’s campaign.

But Italy’s intelligence services told Mr. Barr that they played no such role in the events leading to the Russia investigation, Prime Minister Giuseppe Conte of Italy said in a news conference on Wednesday. Mr. Barr has also contacted government officials in Britain and Australia about their roles in the early stages of the Russia investigation.

Revelations so far about Mr. Durham’s investigation have shown that he has focused in his first months on the accusations that Mr. Trump’s conservative allies have made about the origins of the Russia inquiry in their efforts to undermine it. Mr. Durham’s efforts have prompted criticism that he and Mr. Barr are trying to deliver the president a political victory, though investigators would typically run down all aspects of a case to complete a review of it.