WASHINGTON – The Justice Department agreed Monday to begin turning over "key evidence" from special counsel Robert Mueller's investigation of President Donald Trump to lawmakers, the head of the House Judiciary Committee said.

The House had been scheduled to vote Tuesday to authorize litigation to enforce subpoenas for documents from Attorney General William Barr and former White House counsel Don McGahn. Judiciary Chairman Jerry Nadler, D-N.Y., said that in exchange for access to Mueller's records, lawmakers would delay an effort to hold Barr in contempt.

Nadler said the Justice Department had agreed to give committee members access to Mueller's "most important files," which he said would give them "key evidence that the special counsel used to assess whether the president and others obstructed justice or were engaged in other misconduct."

The Justice Department earlier reached a similar agreement with the Intelligence Committee. Nadler did not offer details about what files were to be turned over.

Kerri Kupec, a Justice Department spokeswoman, said the department was committed to accommodating Congress's legitimate interests in the Mueller inquiry.

“We are pleased the committee has agreed to set aside its contempt resolution and is returning to the traditional accommodation process," she said.

The House will still vote Tuesday on the resolution authorizing litigation in federal court for documents that weren't covered by the compromise, including those from Barr and former White House counsel Don McGahn, Nadler said.

"We have agreed to allow the Department time to demonstrate compliance with this agreement,” Nadler said. “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. If important information is held back, then we will have no choice but to enforce our subpoena in court and consider other remedies.”

Republicans repeated their concern that Nadler acted hastily in having the committee hold Barr in contempt and in pushing for a floor vote for documents.

“The Justice Department has yet again offered accommodations to House Democrats, and I am glad Chairman Nadler — for the first time in months — has finally met them at the negotiating table,” said Rep. Doug Collins of Georgia, the top Republican on the committee.

Trump and congressional Republicans have said the Mueller case is closed and that Democrats should move on. Mueller found no conspiracy between the Trump campaign and Russians who sought repeatedly to influence the 2016 election. Mueller didn't decide whether to charge Trump with obstruction of justice, despite 10 episodes of potential obstruction, and Barr decided no charges were merited.

But House Democrats are eager to explore portions of the report that Barr blacked out, and the underlying evidence that supported the report. The compromise Monday signaled an incremental agreement for lawmakers to get more information that is not yet public.

The committee held a hearing Monday featuring former White House counsel John Dean, who testified in 1973 about the Watergate scandal, about potential obstruction described in the Mueller report.

Nadler said the agreement with the Justice Department didn’t cover all redactions from the Mueller report, including grand-jury information. But he said the House vote Tuesday could lead to McGahn’s testimony.

“It is my expectation that as a result of this authorization that Mr. McGahn will testify here before long,” Nadler said.

Collins said witnesses at the hearing Monday couldn’t provide first-person testimony about the Mueller report, but that he could hear their views on television.

“I could catch your testimony on TV,” Collins said.

Trump tweeted Monday a criticism of Dean and repeated that Democrats wanted a "do-over" on Mueller's inquiry.

"Can’t believe they are bringing in John Dean, the disgraced Nixon White House Counsel who is a paid CNN contributor," Trump said.

More on Congress and special counsel Robert Mueller's report:

House investigations of President Trump hit a wall of delay; demands for records, witnesses are mostly on hold

'Slow-motion constitutional car crash': Trump, Congress battle over investigations with no end in sight

'We're fighting all the subpoenas.' Congress and Trump prepare to battle over wide-ranging probes