Former special counsel Robert Mueller will testify to Congress next month after being subpoenaed by two committees, lawmakers announced Tuesday night, setting up a major showdown that could set the tone for the rest of President Trump’s term.

“The American public deserves to hear directly from you about your investigation and conclusions,” Judiciary Committee Chairman Jerrold Nadler, New York Democrat, and Rep. Adam B. Schiff, California Democrat and chairman of the Permanent Select Committee on Intelligence, said in a joint letter alerting Mr. Mueller that he has been subpoenaed.

The two Democrats said they wanted to get Mr. Mueller to testify voluntarily but were prepared to issue subpoenas, “and we now understand it is necessary to do so.”

They said Mr. Mueller has agreed to comply and will testify in open session — though Mr. Schiff, speaking to CNN on Tuesday evening, said the former special counsel is a reluctant witness.

It’s unclear what he will add to his 448-page report, most of which has been public for two months.

Mr. Mueller, in a farewell statement to the press in May, said the report spoke for itself and warned that he would have nothing to add if called to testify.

“The report is my testimony. I would not provide information beyond that which is already public in any appearance before Congress,” he said at the time.

But Democrats, furious that his report isn’t gaining more traction in the public’s mind, have been eager to create a made-for-television forum to air Mr. Mueller’s findings.

“Americans have demanded to hear directly from the special counsel so they can understand what he and his team examined, uncovered, and determined about Russia’s attack on our democracy, the Trump campaign’s acceptance and use of that help, and President Trump and his associates’ obstruction of the investigation into that attack,” the chairmen said in their joint statement.

In an appearance Tuesday evening on CNN, Rep. Raja Krishnamoorti, Illinois Democrat and a member of the intelligence committee, predicted there would be “a Super Bowl sized audience” for the public hearing.

Mr. Mueller spent nearly two years leading a team that investigated the 2016 election, Russian attempts to interfere in it, and President Trump’s behavior during the campaign and afterward as president.

The special counsel did not find a conspiracy between the Trump campaign and Russia to subvert the election, but he did identify a number of instances of behavior while Mr. Trump was in office that could be seen as attempts to obstruct the Russia investigation itself.

In the end, Mr. Mueller declined to make any recommendations about charges, at least in part because Justice Department policy prohibits charging a sitting president.

Still, he said: “If we had had confidence that the president clearly did not commit a crime, we would have said so.”

Attorney General William Barr and then-Deputy Attorney General Rod Rosenstein, to whom Mr. Mueller reported during his investigation, looked at the report and concluded there wasn’t a prosecutable case to be made.

Democrats vehemently disagree with that reading and hope to entice Mr. Mueller to say so in his appearance.

Rep. Doug Collins of Georgia, the ranking Republican on the Judiciary Committee, said he is eager to hear Mr. Mueller testify and hopes it will put to rest some of the acrimony that still surrounds the investigation.

“I hope the special counsel’s testimony marks an end to the political gamesmanship that Judiciary Democrats have pursued at great cost to taxpayers,” he said. “May this testimony bring to House Democrats the closure that the rest of America has enjoyed for months.”

Mr. Schiff said the committees won’t be bound by the Mueller report in their questioning and can go into other areas.

Mr. Nadler, meanwhile, told CNN on Tuesday evening that he won’t allow the White House and Justice Department to restrict Mr. Mueller’s testimony as they have with such witnesses as former White House communications director Hope Hicks.

The Justice Department has warned that some of the materials Mr. Mueller dealt with in his work and his report are secret because they were gleaned from grand jury proceedings, while other information could tread on ongoing investigations.

The two committee chairmen said they understand those restrictions but that his testimony is too important.

The move should give Democratic leaders some breathing space as they try to contain a growing pro-impeachment movement within their ranks. Led by House Speaker Nancy Pelosi, California Democrat, most of those leaders have urged a slower approach, saying committees must be given a chance to do their fact-finding first.

Rep. Ro Khanna, California Democrat and a prominent liberal lawmaker who has backed Mrs. Pelosi, said the Mueller subpoena was a sign that she has the right approach.

“To the naysayers who have doubted the effectiveness of our committee chairs, this shows measurable and real progress in our methodical and assertive approach in holding the president accountable,” he said on Twitter.

• Victor Morton contributed to this report.

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