Mr. Sessions fended off demands that he resign but agreed to recuse himself from what may be the most important investigation his Justice Department is conducting: of Russian meddling in the election and whether any of Mr. Trump’s associates colluded in those efforts. And that did not end the issue; all nine Democrats on the Senate Judiciary Committee called on Friday for Mr. Sessions to testify about his inaccurate denials that he had met with Russian officials during the campaign.

Part of the problem underlying disputes over such contacts may be Mr. Trump’s pugnacious style, which usually leaves little room for nuance. At a news conference last month, he said that he had “nothing to do with Russia,” and that “to the best of my knowledge, no person that I deal with does.”

In fact, vigorous reporting by multiple news media organizations is turning up multiple contacts between Trump associates and Russians who serve in or are close to Mr. Putin’s government. There have been courtesy calls, policy discussions and business contacts, though nothing has emerged publicly indicating anything more sinister. A dossier of allegations on Trump-Russia contacts, compiled by a former British intelligence agent for Mr. Trump’s political opponents, includes unproven claims that his aides collaborated in Russia’s hacking of Democratic targets.

Current and former American officials have said that phone records and intercepted calls show that members of Mr. Trump’s 2016 presidential campaign and other Trump associates had repeated contacts with senior Russian intelligence officials in the year before the election.

Former diplomats and Russia specialists say it would have been absurd and contrary to American interests for the Trump team to avoid meetings with Russians, either during or since the campaign.

John R. Beyrle, the United States ambassador to Moscow from 2008 to 2012, said he feared that “we’re beginning to out-Russian the Russians” by treating all contacts as suspicious. When he returns to Russia now, he said, “this real anti-Western, anti-American frenzy” prompts some old acquaintances to refuse to meet him because they worry about being tagged as too friendly to the United States.

“That’s the last behavior we should model — that simply meeting with a Russian official is wrong, without any knowledge of what was said,” Mr. Beyrle said.