One possible area of dispute is the description of the Russians involved. Some law enforcement officials took issue with the Times account in the days after it was published, saying that the intelligence was still murky, and that the Russians who were in contact with Mr. Trump’s advisers did not meet the F.B.I.’s black-and-white standard of who can be considered an “intelligence officer.”

But several former American intelligence and law enforcement officials have said that other American agencies have a broader definition, especially when it comes to Russia. They said that President Vladimir V. Putin uses an extensive network of government officials and private citizens with deep links to Russian spy services who supplement the intelligence apparatus and report back to the Kremlin. At least some of the contacts, they said, involved Russians who fit into this category.

In testimony last month before the House Intelligence Committee, John O. Brennan, the former C.I.A. director, said he became concerned last year about direct attempts by the Russian government to recruit members of Mr. Trump’s campaign.

“I encountered and am aware of information and intelligence that revealed contacts and interactions between Russian officials and U.S. persons involved in the Trump campaign that I was concerned about because of known Russian efforts to suborn such individuals,” he told lawmakers. “And it raised questions in my mind again whether or not the Russians were able to gain the cooperation of those individuals.”