The hearings will most likely be aired live and in full on network and cable television. With other potential witnesses off limits for now, Mr. Mueller possesses perhaps the singular authority to shift the dynamic in Washington and change the minds of Americans across the country who long since cast their lot with Mr. Trump or his critics.

“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,” Mr. Nadler and Mr. Schiff said in a joint statement.

The question is what Mr. Mueller will be willing to say.

From the time he took over the F.B.I.’s investigation of Russia’s election meddling and possible ties to the Trump campaign in May 2017, Mr. Mueller, 74, has been one of the most vexing figures in American public life. He conducted his work in absolute private, despite incessant attacks by Mr. Trump in public and from within the White House, and ultimately issued a lengthy report that raised as many questions as it answered.

In the report, Mr. Mueller detailed Russia’s disinformation and hacking campaigns to sow chaos in the American political system, harm Hillary Clinton’s 2016 presidential campaign and eventually bolster Mr. Trump. Though he detailed more than 100 contacts between Trump associates and various Russian figures and painted a picture of a campaign that welcomed the foreign assistance, the special counsel ultimately concluded that there was insufficient evidence to charge anyone with conspiring with the Russians to undermine the 2016 election.

Mr. Mueller’s team also extensively investigated whether Mr. Trump’s attempts to thwart its work amounted to obstruction of justice. The special counsel’s report documented 10 such episodes — including orders by Mr. Trump to fire Mr. Mueller, to constrain his investigation and to alter records about what he had done.

Ultimately, the members of Mr. Mueller’s team concluded that because Justice Department policy prohibits indicting a sitting president, they could not determine whether Mr. Trump’s actions had been criminal. But they also clearly stated that they could not exonerate the president of wrongdoing, either, and that the Constitution provides another means of adjudicating possible presidential wrongdoing: Congress.