Representative Jackie Speier, a California Democrat who sits on the House Intelligence Committee, lamented that lawmakers had spent “weeks not talking about Russia, and instead talking about whether he was wiretapped.”

Congressional leaders have not indicated how they envision their inquiries ending, and so far they are still seeking common ground on how to begin.

“It is a very different time,” said Senator Ron Wyden, Democrat of Oregon and a member of the Senate Intelligence Committee. He contrasted the Russia inquiries with investigations into the Watergate break-in or abuses by intelligence agencies, which were bipartisan efforts that operated on a clear track.

Mr. Wyden was hesitant to lay out a specific timeline for the Senate investigation. “That’s the way to really lose credibility,” he said. “I think you let the facts drive the answer to that.”

Representatives Devin Nunes, Republican of California and the chairman of the House Intelligence Committee, and Adam B. Schiff, Democrat of California and the committee’s ranking member, have made a point of appearing publicly in sync on the Russia investigation, despite their sharp political differences. Both believe that the House investigation is vital, but for different reasons: Mr. Nunes’s primary concern so far has been leaks of classified information, whereas Mr. Schiff has tried to keep the focus on Russian meddling. He has also had to manage other Democrats who want to prioritize digging into Mr. Trump’s ties to Russia and who have called for the committee to subpoena the president’s tax returns.

As for the F.B.I., American officials said there was no sign that the bureau’s work might end anytime soon. Counterintelligence investigations can last for years, and they rarely become public or lead to criminal charges. Agents and analysts, working with their counterparts at the C.I.A. and other intelligence agencies, are still trying to figure out the scope of Russian intelligence operations related to the election, including who was involved and how to prevent a repeat.

Exploring any connections between Mr. Trump’s associates and Russians, officials say, is only one aspect. Unlike the criminal cases the F.B.I. investigates — from financial crimes to mafia grifting — the bureau in counterintelligence cases focuses less on “solving” a case than on better understanding the nature of intelligence activity.