[Want to understand impeachment? Read our explainer.]

“We’re beyond talking about this in terms of political implications,” Representative Jim McGovern of Massachusetts told WGBH radio in Boston, endorsing an impeachment inquiry. “We have to do what’s right.”

Mr. McGovern, the chairman of the powerful Rules Committee, is one of the highest-ranking House Democrats to back the idea, but there were other new supporters, too, pushing the total number of lawmakers in favor of an impeachment inquiry well above 40. Representative Bennie Thompson of Mississippi, the chairman of the Homeland Security Committee, said Mr. Trump had “egregiously obstructed justice” and warranted the inquiry. Representative Chellie Pingree of Maine urged Congress to “continue its own investigations in the face of unprecedented obstruction and move toward an impeachment inquiry.”

Top House leaders, though, continued to be more cautious, arguing that Democrats had not yet built the kind of case that would be necessary to warrant such significant action. Speaker Nancy Pelosi, who has tried to hold back an impeachment inquiry, said Wednesday that “nothing is off the table.”

“But,” she continued at the Commonwealth Club in San Francisco, “we do want to make such a compelling case, such an ironclad case, that even the Republican Senate, which at the time seems not to be an objective jury, will be convinced of the path we have to take as a country.”

She does not believe her colleagues have yet done that.

Instead, top Democratic leaders allied with Ms. Pelosi used Mr. Mueller’s remarks as a chance to reiterate the importance of having the special counsel testify before Congress. The sight of Mr. Mueller describing his findings on live television deepened Democratic convictions that putting him on the witness stand would help convince Americans of the gravity of Russia’s election interference and Mr. Trump’s efforts to thwart the investigation.