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But the F.B.I. has taken seriously the possibility that Russian spies would target American politicians. In a secure room at the Capitol, an F.B.I. agent told Mr. Rohrabacher in 2012 that Russian spies were trying to recruit him as an “agent of influence” — someone the Russian government might be able to use to steer Washington policy-making, former officials said.

Mr. Rohrabacher said in a telephone interview on Thursday that the meeting had focused on his contact with one member of the Russian Foreign Ministry, whom he recalled meeting on a trip to Moscow. “They were telling me he had something to do with some kind of Russian intelligence,” Mr. Rohrabacher said. He recalled the F.B.I. agent saying that Moscow “looked at me as someone who could be influenced.”

Law enforcement officials did not think that Mr. Rohrabacher was actively working with Russian intelligence, officials said, rather that he was being targeted as an unwitting player in a Russian effort to gain access in Washington, according to one former American official. The official said there was no evidence that Mr. Rohrabacher was ever paid by the Russians.