A May 2016 email to the campaign adviser, Rick Dearborn, bore the subject line “Kremlin Connection.” In it, the N.R.A. member said he wanted the advice of Mr. Dearborn and Senator Jeff Sessions of Alabama, then a foreign policy adviser to Mr. Trump and Mr. Dearborn’s longtime boss, about how to proceed in connecting the two leaders.

Russia, he wrote, was “quietly but actively seeking a dialogue with the U.S.” and would attempt to use the N.R.A.’s annual convention in Louisville, Ky., to make “‘first contact.’” The email, which was among a trove of campaign-related documents turned over to investigators on Capitol Hill, was described in detail to The New York Times.