WASHINGTON — Twelve days after a young Russian gun-rights activist gained access to some of America’s most prominent conservatives, at an elegant dinner near the Capitol, a Republican operative was eager to keep the momentum going.

In a February 2017 email, the operative, Paul Erickson, proposed another “U.S./Russia friendship” dinner. He noted that the activist, Maria Butina, who now is accused of being a covert Russian agent, was making an “ever-expanding circle of influential friends.”

Ms. Butina, he wrote in the email, had just met Susan Eisenhower, the granddaughter of President Dwight D. Eisenhower, during a visit to Gettysburg College in Pennsylvania. The Russian woman had also gotten to know the ex-wife of a supermarket heir, who had endowed an institute dedicated to furthering American-Russian relations, and the “silky smooth” former Russian diplomat who ran it.

Then there was the recipient of the email, George O’Neill Jr., a Rockefeller relative and conservative writer. He was helping pay Ms. Butina’s bills, said a person familiar with their relationship, and hoped to make her the centerpiece of his own project to improve America’s ties to Russia.