Mr. Flynn has admitted that he requested that Russia not escalate tensions between the countries after the outgoing Obama administration imposed sanctions against Russia for its interference in the 2016 presidential race. Russia agreed to not retaliate, an unusual decision that Mr. Trump himself praised.

But in his interview with the F.B.I., Mr. Flynn claimed that he did not remember ever asking Mr. Kislyak that Russia restrain its response, the agents wrote in the document, known as a 302. He told them that he did not even know about the Obama administration's decision to expel dozens of Russian diplomats and to seize two Russian-owned properties in the United States because at the time the sanctions were imposed, he was on vacation in the Dominican Republic, without access to television or to his government-issued BlackBerry phone.

Mr. Flynn also has acknowledged lying to the agents about his conversations with Mr. Kislyak involving Russia's impending vote in the United Nations on an Egyptian-sponsored resolution to condemn Israeli settlements in the West Bank. He has admitted that he asked that Russia either delay or oppose the resolution.

But in their account of their interview, the agents stated that Mr. Flynn said he had merely inquired about Russia's views on the resolution.

Asked whether he had advocated that Russia take any particular position, "FLYNN answered, 'No,'" the agents wrote. Instead, he "stated the conversations were along the lines of where do you stand, and what's your position," they said.

Mr. Flynn also said that he had no particular fondness for Russia but communicated with Mr. Kislyak because "maintaining trusted relationships within foreign governments is important," the agents stated.

The interview both alarmed and perplexed agents at the F.B.I., then in the midst of a highly sensitive counterintelligence investigation targeting Mr. Flynn and three other associates of Mr. Trump's.