Democrats struggled to find a path ahead, with some urging the party to turn its attention to policy differences with Mr. Trump. Speaker Nancy Pelosi has credited such a strategy with fueling last year’s midterm election victories and said she opposed trying to impeach the president “unless there’s something so compelling and overwhelming and bipartisan.” She plans to unveil a health care plan on Tuesday.

“The report vindicates Nancy Pelosi’s judgment of proceeding with deliberateness and caution and focusing on issues that we can deliver for the American people,” said Representative Ro Khanna, Democrat of California and a leading liberal voice in the House.

Republicans faced their own choice. After two years shadowed by Mr. Mueller, Mr. Trump has the opportunity to reset his presidency, but as he strode with new confidence into a post-Mueller world, he appeared more intent on payback.

Stephen K. Bannon, his former chief strategist, predicted that Mr. Trump “is going to go full animal” now that Mr. Mueller has wrapped up. The president, Mr. Bannon told Yahoo News, will “come off the chains” and use the findings to “bludgeon” his opposition.

Others close to the White House urged the president not to do that but instead focus on his own agenda. “The president has a unique historical opportunity, while in his re-election cycle, to reconnect to millions of Americans who have assumed he was guilty of serious wrongdoing, due to the unrelenting irresponsible media coverage of fake collusion,” said Matt Schlapp, the chairman of the American Conservative Union.

Senator Lindsey Graham, Republican of South Carolina, who golfed with Mr. Trump in Florida last weekend, agreed. “My advice to the president, for whatever it’s worth, is that you are probably stronger today than you have been at any time in your presidency,” he said, adding, “And if I were you, Mr. President, I would focus on what’s next for the country.”

Instead, Mr. Graham said, the president should leave it to him to go after the authors of the Russia investigation. As chairman of the Senate Judiciary Committee, Mr. Graham announced that he would investigate anti-Trump bias at the F.B.I. and Justice Department and called on Mr. Barr to appoint a second special counsel to study the same issues.