Nearly a dozen lawmakers came out for beginning impeachment proceedings after Mr. Mueller’s testimony, with four legislators — Representatives Derek Kilmer, Suzan DelBene, Denny Heck and Kim Schrier, all of Washington State — calling for an inquiry after Mr. Nadler’s remarks. That pushes the total number of lawmakers in favor of doing so to more than 100.

But much of the caucus has remained skeptical of the political implications of such a move that would doubtless end with an acquittal in the Senate, and Speaker Nancy Pelosi has urged caution. “We will proceed when we have what we need to proceed,” she told reporters on Friday. “Not one day sooner.”

The Judiciary Committee has toyed with the idea of impeachment for months, holding hearings and subpoenaing witnesses. In an escalation carrying perhaps the most overt political implications yet, on Friday the panel asked a federal judge to unseal grand jury secrets related to Mr. Mueller’s investigation, using the court filing to declare that lawmakers had already in effect begun an impeachment investigation of Mr. Trump.

“Too much has been made of the phrase ‘an impeachment inquiry,’” Mr. Nadler said at a news conference on Friday. “We are doing what our court filing says we are doing, what I said we are doing, and that is to say we are using our full Article I powers to investigate the conduct of the president and to consider what remedies there are. Among other things we will consider, obviously, are whether to recommend articles of impeachment.”

Mr. Trump took aim at Mr. Nadler on Saturday night, fuming on Twitter that “we gave Nadler and his Trump hating Dems the complete Mueller Report (we didn’t have to), and even Mueller himself, but now that both were a total BUST, they say it wasn’t good enough.”