But the president’s allies have seized on the F.B.I.’s conduct in opening the inquiry as potentially problematic. Attorney General William P. Barr prompted alarm among defenders of the F.B.I. by accusing the bureau this year of spying on the campaign.

The F.B.I. director, Christopher A. Wray , who was appointed in 2017, has said he would not use the term spying to describe F.B.I. activities in 2016 . The Mueller report reaffirmed the factors that the F.B.I. used to open its investigation, and Mr. Horowitz’s findings are also said to show that the F.B.I. acted properly in opening the inquiry.

F.B.I. officials started the investigation, code-named Crossfire Hurricane, in July 2016 after learning that a Russian intermediary had offered information that could damage Hillary Clinton to a Trump campaign aide, George Papadopoulos. The F.B.I. eventually began looking at four Trump campaign advisers who had ties to Russia, including Mr. Papadopoulos, and as law enforcement and intelligence officials were realizing the extent of the Kremlin’s ongoing campaign to sabotage the election.

The F.B.I. was cognizant of being seen as interfering with a presidential campaign, and former law enforcement officials are adamant that they did not investigate the Trump campaign organization itself or target it for infiltration. But agents had to investigate the four advisers’ ties with Russia, and the people they did scrutinize all played roles in the Trump campaign.

Mr. Trump and his allies have pointed to some of the investigative steps the F.B.I. took as evidence of spying, though they were typical law enforcement activities. For one, agents had an informant, an academic named Stefan A. Halper , meet with Mr. Page and Mr. Papadopoulos while they were affiliated with the campaign. The president decried the revelation as an “all time biggest political scandal” when it emerged last year.

The F.B.I. did have an undercover agent who posed as Mr. Halper’s assistant during a London meeting with Mr. Papadopoulos in August 2016. And indeed, another Trump adviser, Peter Navarro , reportedly pushed Mr. Halper for an ambassadorship in the Trump administration.

Mr. Halper turned down the job and told the F.B.I. that Mr. Navarro had made the overture, according to a person familiar with the offer.