Mr. Trump first mentioned that he “had a long and very good conversation” with Mr. Putin in a tweet, in which he also said that the subjects discussed included “even the ‘Russian Hoax.’” When the subject of the Mueller report and Russia’s role in the election came up during the call, Mr. Trump later explained, Mr. Putin “actually sort of smiled when he said something to the effect that it started off as a mountain and ended up being a mouse. But he knew that because he knew there was no collusion whatsoever.”

A White House official later clarified that it was not a video call; Mr. Trump meant to say that Mr. Putin had “laughed, chuckled” rather than smiled.

Mr. Putin has long denied that Russia interfered in the election, though he has been frank that he was rooting for Mr. Trump to win in 2016. Standing next to Mr. Trump in Helsinki, Finland, last July, he said, “Yes I did, yes I did, because he talked about bringing the U.S.-Russia relationship back to normal.”

The summary of the call released by the Kremlin said the “two heads of state expressed satisfaction with the businesslike and constructive nature of the conversation.” But the statement also revealed a few potential fissures. On Venezuela, it condemned “outside interference in the country’s internal affairs” and added that “attempts to change the government in Caracas by force undermine prospects for a political settlement of the crisis.”

The statement also stressed the need to lift sanctions on North Korea in return for “good faith” moves to disarm its nuclear arsenal — a step-by-step approach that Mr. Trump has resisted in his two meetings with the North Korean leader, Kim Jong-un. He has pushed a deal in which the North would agree to give up all its weapons for a lifting of sanctions. But Mr. Putin, who met with Mr. Kim in Vladivostok, Russia, on April 25, appears to be positioning himself as a player in the nuclear negotiations.

Just hours after the call, North Korea launched several short-range projectiles, which followed the mid-April test of what Pyongyang called a “tactical guided weapon.” The most recent move is likely to ratchet up tensions as Mr. Kim seeks a bargaining chip in talks with the United States.

Mr. Trump made no mention of his and Mr. Putin’s differences over North Korea in describing the call, which lasted more than an hour. In the past, he has steadfastly avoided criticizing Mr. Putin, even when he authorized tough moves against Russia, like approving the sale of lethal defensive weapons to the Ukrainian military for its battle against Russian-backed forces, or expelling 60 Russian diplomats to retaliate for Moscow’s poisoning of a former spy on British soil.