WASHINGTON — The chairman of the House Judiciary Committee issued a subpoena on Friday demanding that the Justice Department hand over an unredacted version of Robert S. Mueller III’s report and the evidence underlying it by May 1, and pledged “major hearings” on its findings.

The subpoena, one of the few issued thus far by House Democrats, escalates a fight with Attorney General William P. Barr over what material Congress is entitled to see from the special counsel’s nearly two-year investigation. The chairman, Representative Jerrold Nadler of New York, asked for all evidence obtained by Mr. Mueller’s investigators, including summaries of witness interviews and classified intelligence — and indicated he intended to air it to the public.

“Even the redacted version of the report outlines serious instances of wrongdoing by President Trump and some of his closest associates,” Mr. Nadler said in a statement. “It now falls to Congress to determine the full scope of that alleged misconduct and to decide what steps we must take going forward.”

The subpoena was sent as House Democrats, who have the power to initiate impeachment proceedings if they so choose, debate how to proceed with the new evidence handed over Thursday by Mr. Mueller. Democratic-led committees have already initiated their own investigations of Russian election influence, as well as obstruction of justice and abuse of power, which can incorporate the findings in the shorter term. But there were also new calls in the wake of the report from the party’s left flank — including Senator Elizabeth Warren, a Massachusetts Democrat running for president — to go further and open a formal impeachment inquiry.