That trip last July was a catalyst for the F.B.I. investigation into connections between Russia and President Trump’s campaign, according to current and former law enforcement and intelligence officials.

It is unclear exactly what about Mr. Page’s visit drew the F.B.I.’s interest: meetings he had during his three days in Moscow, intercepted communications of Russian officials speaking about him, or something else…

Mr. Page’s relationship with Mr. Trump appears to have been fleeting. According to former Trump campaign officials, the two men have never met, though Mr. Page has said he attended some meetings where Mr. Trump was present.

But last spring, when Republican foreign policy experts were distancing themselves from Mr. Trump, Mr. Page served a purpose for the flailing Trump campaign. Dismissing the notion that his campaign was bereft of foreign policy expertise, the candidate read aloud a list of five people who had offered to advise him on world affairs — including “Carter Page, Ph.D.”