Mr. Amash’s conclusions track closely with those of many Democrats. While Speaker Nancy Pelosi has sought to block attempts to impeach Mr. Trump based on the findings of the Mueller report, she declared her openness last week to initiating an impeachment inquiry as a means of forcing administration officials to comply with the subpoenas of the six House committees investigating Mr. Trump’s conduct.

Earlier on Saturday, Representative Jamie Raskin, Democrat of Maryland, who serves on the House Judiciary Committee, said that an increasing number of his colleagues were moving toward a conclusion that some kind of impeachment proceeding was inevitable.

“We have to keep this in proportion with everything else we’re doing, but believe me, the anger and frustration is growing, not just in the public, but within the ranks of Democrats, too,” he said during an interview on MSNBC. “I believe that we are headed toward an impeachment inquiry.”

This is not the first time Mr. Amash, who considers himself a libertarian and strict constitutionalist, has defied the White House and bucked his party’s Capitol Hill leadership. Mr. Amash was one of 14 Republicans to side with Democrats in their unsuccessful attempt to override the president’s first veto, which upheld an emergency declaration to divert funding from other federal projects to build a wall along the southwestern border.

Republican leaders in both chambers have griped privately about Mr. Trump’s behavior but have publicly fallen in line behind the president. Mr. Trump has seized on Mr. Mueller’s finding that his campaign did not coordinate with Russia to declare that the investigation was an exoneration. (In fact, the report stopped short of clearing the president on the question of whether he illegally obstructed justice.)

On Thursday, Ms. Pelosi said she would consider impeachment only as a means of compelling Mr. Barr and Donald F. McGahn II, the former White House counsel who cooperated extensively with the special counsel’s inquiry, to testify — despite Mr. Trump’s blanket call for current and former aides to stonewall all requests by Democrats for testimony or documents.

But first, she added, House committees must exhaust all their legal and legislative options. “First we ask, then we subpoena friendly,” she said. “Then we subpoena otherwise, and then we see what we get. So let’s not leapfrog over what we think should be the path that should be taken.”