The statements from the Justice Department’s top official and one of his key investigators gave ammunition to Mr. Trump’s supporters to dispute a major finding in the long-awaited report by Mr. Horowitz that was one of the few bright spots for the F.B.I. But it drew criticism from the F.B.I.’s supporters.

“I don’t understand how Barr can on the one hand lavish praise on the inspector general and his team of lawyers and investigators, and in the next breath seek to undermine its key finding that the investigation was authorized and validly predicated,” said Michael Bromwich, a former Justice Department inspector general who is now a lawyer in private practice. Mr. Horowitz has harshly criticized one of his clients, the former F.B.I. deputy director Andrew G. McCabe, for violations of the Justice Department’s media policy.

“They either got it right or they didn’t,” Mr. Bromwich said.

Mr. Horowitz found that the F.B.I. had adequate reason in 2016 to lawfully open a full investigation into whether Trump campaign associates were wittingly or unwittingly helping Russia to interfere in the election. Called Crossfire Hurricane, the investigation eventually focused on four Trump campaign associates, two of whom were already the subjects of continuing Justice Department investigations.

The F.B.I. opened the inquiry amid a rash of leaked emails that had been stolen from the Democratic National Committee, and days after receiving intelligence that a Trump campaign adviser at the time, George Papadopoulos, had told Australian diplomats that a Russian had intermediary had offered information that could damage Hillary Clinton’s campaign.

Only the tip from the Australian government was officially used “to predicate the opening of the Crossfire Hurricane investigation,” Mr. Horowitz said — and that was enough information to open the inquiry. His conclusion undercut accusations by the president and his allies that F.B.I. officials had carried out a politicized conspiracy to sabotage his campaign.

Mr. Horowitz also said that the F.B.I. followed all policies when it used informants to carry out that work. He noted that the bureau’s standards were very low, and he initiated an audit of how it would handle applications to wiretap Americans citizens in the future.

Christopher A. Wray, the director of the F.B.I., said that he accepted all of the report’s findings, including that officials had enough reason to open the investigation, as did other F.B.I. defenders.