© Doug Mills/The New York Times The Justice Department has agreed to provide Congress with key evidence collected by Robert S. Mueller III, the former special counsel.

WASHINGTON — The Justice Department, after weeks of tense negotiations, has agreed to provide Congress with key evidence collected by Robert S. Mueller III that could shed light on possible obstruction of justice and abuse of power by President Trump, the House Judiciary Committee said on Monday.

The exact scope of the material the Justice Department has agreed to provide was not immediately clear, though the committee signaled that it could be a breakthrough after weeks of wrangling over those materials and others that the Judiciary panel demanded under subpoena. The Trump administration’s blockade of the material had ground the Democratic investigations of Mr. Trump’s possible obstruction of justice and abuse of power to a halt.

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“These documents will allow us to perform our constitutional duties and decide how to respond to the allegations laid out against the president by the special counsel,” Representative Jerrold Nadler of New York, the committee chairman, said in a statement.

Mr. Nadler said he expected the department to begin sharing some of the material Monday afternoon and that all members of the committee would be able to view it privately.

The agreement appears to have been foreshadowed in an exchange of letters in recent weeks between the committee and the department. In a May 24 letter outlining a proposed compromise Mr. Nadler wrote that he was “prepared to prioritize production of materials that would provide the committee with the most insight into certain incidents when the special counsel found ‘substantial evidence’ of obstruction of justice.”

Those incidences include Mr. Trump’s attempts to fire Mr. Mueller, the special counsel; his request that Donald F. McGahn II, the former White House counsel, create “a fraudulent record denying that incident”; and Mr. Trump’s efforts to get former Attorney General Jeff Sessions to undo his recusal and curtail the scope of the special counsel inquiry.

After weeks of objections, the Justice Department said it found the proposal reasonable and would work with the committee to share the materials in question, but only if the House would back off holding Attorney General William P. Barr in contempt of Congress for his defiance of the subpoena in question.

It appears Democrats were willing to do so. The House still plans to vote on Tuesday to authorize the committee to go to a federal court against Mr. Barr to seek full enforcement of its subpoena and to petition a judge to unseal grand jury secrets related to the case for Congress. But in a sign of the newfound cooperation, the House will not formally vote to hold Mr. Barr in contempt of Congress, leveling a criminal accusation against him. Mr. Nadler hinted that Democrats could hold off on filing a lawsuit for now, as well.

“We have agreed to allow the department time to demonstrate compliance with this agreement. If the Department proceeds in good faith and we are able to obtain everything that we need, then there will be no need to take further steps,” Mr. Nadler said. “If important information is held back, then we will have no choice but to enforce our subpoena in court and consider other remedies.”

News of the deal also comes just hours before the committee is scheduled to convene the first of a series of hearings focused on the findings of Mr. Mueller’s obstruction of justice investigation — a much-anticipated session that underscores the Democrats’ dilemma in the wake of Mr. Mueller’s report.

Because the Trump administration has blocked relevant witnesses from testifying, Monday’s session will star John W. Dean, a former White House counsel who turned against President Richard M. Nixon during the Watergate affair, and former federal prosecutors, who will assess the implications of the special counsel’s findings. The testimony is expected to be limited to the contents of Mr. Mueller’s 448-page report already voluntarily made public by Mr. Barr.

Weeks ago, the Judiciary Committee requested — and then subpoenaed — the full text of Mr. Mueller’s report without redactions, as well as all of the evidence underlying it. Mr. Barr initially refused and after negotiations broke down, Mr. Trump asserted executive privilege over all the material. Democrats then voted to recommend the House hold Mr. Barr in contempt.

But in recent weeks, the Justice Department appeared amenable to a proposed compromise that would give the committee access to F.B.I. interview summaries with key witnesses, contemporaneous notes taken by White House aides, and certain memos and messages cited in the report.

The more limited request outlined in recent weeks includes the F.B.I. summaries — called 302 reports — with Mr. McGahn, who served as a kind of narrator for Mr. Mueller as he assembled an obstruction case. Mr. Mueller ultimately concluded that Justice Department policy prevented him from contemplating charges against Mr. Trump and instead left action to Congress.

Democrats asked for summaries from interviews with Annie Donaldson, Mr. McGahn’s chief of staff; Hope Hicks, the former communications director; Reince Priebus and John F. Kelly, former White House chiefs of staff; Michael D. Cohen, Mr. Trump’s one-time fixer and personal lawyer; and Mr. Sessions, among others.

Democrats had also requested detailed notes taken by Ms. Donaldson about White House meetings and Mr. McGahn’s interactions with the president that proved pivotal for Mr. Mueller’s team, as well as notes taken by Joseph Hunt, Mr. Sessions’s chief of staff when he was attorney general. Other documents in the narrowed request included a draft letter justifying the firing of James B. Comey as F.B.I. director; a White House counsel memo on the firing of Michael Flynn as national security adviser; and other documents created by the White House.