The F.B.I. also obtained a wiretap order from the Foreign Intelligence Surveillance Court targeting Carter Page, a former Trump campaign adviser. Its application partly relied upon unverified information about Trump ties to Russia generated by an investigator who was indirectly paid by Democrats.

The review is also likely to entangle the C.I.A. director, Gina Haspel, who was the agency’s London station chief at a seminal moment in the F.B.I.’s investigation. In late July 2016, the Australian government told the United States Embassy in London that George Papadopoulos, a Trump campaign adviser, had told an Australian diplomat that Russia had damaging information about Hillary Clinton in the form of stolen emails before WikiLeaks published them. It remains unclear if Ms. Haspel was aware at the time of the information the Australians had provided to the United States.

That information partly formed the basis for opening the Russia investigation. F.B.I. agents traveled the following month to London to interview the diplomat and then mounted an operation targeting Mr. Papadopoulos and several other Trump campaign aides with personal ties to Russia. The following spring, Mr. Mueller was appointed special counsel to take over the investigation after Mr. Trump fired James B. Comey as F.B.I. director.

Mr. Durham’s assignment is to review all intelligence collection activities related to the Trump campaign, the person said.

Mr. Barr, who asked Mr. Durham to oversee that review several weeks ago, is also taking a personal role in it, the person said. He has been discussing it with Ms. Haspel; Christopher A. Wray, the F.B.I. director; and Dan Coats, the director of national intelligence.

When the FISA wiretap targeting Mr. Page came to light and Mr. Trump’s allies portrayed it as an abuse of power, the Justice Department — under Rod J. Rosenstein, then the deputy attorney general — referred the matter to Mr. Horowitz, the inspector general, for a review.

Mr. Rosenstein also asked John W. Huber, an Obama administration holdover whom Mr. Trump had reappointed as the United States attorney for Utah, to look at the FISA issues, along with several other politically charged matters. But it is not clear that Mr. Huber has done much on the issue yet, possibly waiting for Mr. Horowitz to complete his review first. Mr. Durham will now take over the FISA review assignment from Mr. Huber as part of his broader review, the person said.