Also along for the Russia trip were Joseph R. Gregory, co-chairman of the N.R.A.’s Golden Ring of Freedom, a group for donors of $1 million or more; and Pete Brownell, then the organization’s first vice president, who would later become president.

Congressional scrutiny of the N.R.A. has intensified since Ms. Butina pleaded guilty last month to conspiring to act as a foreign agent, in a deal with the United States attorney’s office in Washington. She admitted to being part of a Russian-backed effort to use the N.R.A. to influence American politics. Two Senate committees are also investigating the N.R.A.’s ties to Russia, as is the House Intelligence Committee, and the Federal Election Commission initiated a preliminary inquiry last year. Three past N.R.A. presidents — Mr. Keene, Mr. Cors and Mr. Brownell — have been asked for interviews in the inquiries.

A critical question for investigators is the extent of the N.R.A.’s financial ties to Russia. While the N.R.A. has turned over thousands of pages of records in the Senate inquiries, those documents do not include the organization’s closely held donor records; it is possible, however, that federal investigators have obtained the organization’s tax records from the Internal Revenue Service.

Responding to questions from the Senate Finance Committee, the N.R.A. said last year that since 2015 it had brought in roughly $2,500 “from people associated with Russian addresses” or Russian nationals living in the United States. But that left open the question of money that may have come from shell companies or other less overt sources.

“The N.R.A. should provide the financial documents and other records necessary to explain the scope of their activities,” Senator Ron Wyden, Democrat of Oregon and the committee’s ranking member, said in a statement. “The prospect of N.R.A. or N.R.A. officials abusing nonprofit status to work with a hostile regime and undermine our democracy is central to my investigation.”

The N.R.A.’s outside counsel, Mr. Brewer, said that after an internal review, the group “believes that no foreign money made its way into the organization for use in the 2016 presidential election.” Any suggestion that the group took in Russian money, he said, “fails to appreciate the steps the N.R.A. takes to guard against such an unwanted event.”

With Democrats now controlling the House, an inquiry led by the House Intelligence Committee has new life.