Washington (CNN) House Judiciary Chairman Jerry Nadler said Monday that he has struck a deal with the Justice Department to begin providing Congress with some documents from the Mueller report related to obstruction of justice, putting off a looming court showdown between House Democrats and Justice over the report.

The court fight to enforce a subpoena to Attorney General William Barr is no longer necessary -- at least for the time being -- as a result of the agreement the committee struck with the Justice Department, Nadler said. Details about which documents would be provided to the committee were not disclosed, but the New York Democrat said the agreement would allow all Judiciary Committee members to see "Robert Mueller's most important files ... providing us with key evidence that the Special Counsel used to assess whether the President and others obstructed justice or were engaged in other misconduct."

"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," Nadler said.

Nadler announced the agreement ahead of a vote scheduled for Tuesday, when the House is expected to approve a resolution to go to court to enforce its subpoenas for Barr and former White House counsel Don McGahn.

Tuesday's vote is still happening and the text of the resolution will not change, according to a senior Democratic aide, but Nadler said the committee would not take court action against Barr unless the Justice Department stopped cooperating.

Nadler said in a statement that he would "hold the criminal contempt process in abeyance for now" as a result of the agreement. But the House resolution introduced last week did not include a criminal contempt citation against Barr -- it was only a resolution to go to court to enforce the subpoenas of Barr and McGahn.

"I see no need to resort to the criminal contempt statute to enforce our April 19 subpoena, at least for now, so long as the Department upholds its end of the bargain," Nadler said at a Monday hearing.

"But our arrangement with the Department does not extend to the full scope of our request for the full Mueller report and its underlying materials, including grand jury information, nor does it extend to our demand that Don McGahn, a key fact witness, testify before this committee," he added.

Department of Justice spokeswoman Kerri Kupec praised Nadler's decision.

"We are pleased the Committee has agreed to set aside its contempt resolution and is returning to the traditional accommodation process," she said in a statement. "The Department of Justice remains committed to appropriately accommodating Congress's legitimate interests related to the Special Counsel's Investigation and will continue to do so provided the previously voted-upon resolution does not advance."

Later Monday, Democratic and Republican staffers went to the Justice Department to begin reviewing the documents, per multiple sources with knowledge of the review told CNN.

Watergate's John Dean testifies before Judiciary panel

Shortly after announcing the agreement to obtain some Mueller report documents, the House Judiciary Committee gaveled into a hearing with former Nixon White House counsel John Dean, a CNN contributor, and former federal prosecutors to discuss "lessons" from the Mueller report.

Dean's appearance prompted several attacks from President Donald Trump, both on Twitter and to reporters. "John Dean's been a loser for many years," Trump said on Monday.

At the hearing Dean, who was a key witness in the Watergate case, evoked similarities between that case and Mueller's investigation.

"In many ways the Mueller report is to President Trump what the so-called Watergate road map, officially titled the grand jury report ... was to President Richard Nixon," Dean said. "Stated a little differently, special counsel Mueller has provided this committee with a road map."

The hearing was the first in a series that the House Judiciary and Intelligence Committees are planning to hold to highlight the Mueller report publicly. Dean noted at the outset he was "not a fact witness," but argued he could provide a historical perspective.

Democrats walked Dean and the former prosecutors through the excerpts of the Mueller report, reading passages aloud and asking the witnesses -- who argued Trump should have been charged with obstruction of justice -- to weigh in.

"The facts contained in that report would be sufficient to prove all of the elements necessary to charge multiple counts of obstruction of justice," said Joyce White Vance, a former US attorney in Alabama. "The evidence is not equivocal, nor is the charging decision a close call. And I would be willing to personally indict the case, and to try the case. I would have confidence that the evidence would be sufficient to obtain a guilty verdict and to win on appeal."

But Republicans questioned why a key witness from the Nixon era was speaking to them about the Mueller report, seizing on his statement that he was not a fact witness and noting that his long public record of commentary criticizing the President. Several Republicans noted that Dean was convicted during Watergate, comparing him to a witness the committee heard from earlier this year, the President's former lawyer Michael Cohen.

"What I really regret Mr. Dean is that you're here as a prop, you are functionally here as a prop, because they can't impeach President Trump because 70% of Democrats want something that 60% of Americans don't," said Rep. Matt Gaetz, a Florida Republican and close Trump ally. "So they're in this no-win situation and you sit before us here with no knowledge of a single fact on the Mueller report on a hearing entitled 'Lessons From the Mueller Report.'"

First signs of agreement between Judiciary panel, DOJ

Monday's agreement is the first sign of a thaw between the House Judiciary Committee and the Justice Department, which have been battling over the special counsel's report since Robert Mueller ended his investigation in March

The agreement with the Judiciary Committee follows a similar accord struck between the Justice Department and House Intelligence Chairman Adam Schiff, a California Democrat, who said last week that his panel had begun reviewing a set of counterintelligence documents from the special counsel's investigation in response to Schiff's subpoena.

In a letter last month, Nadler said he was willing negotiate over the scope of the subpoena and accept a smaller subset of documents out of Mueller's evidence, including FBI summaries of key interviews with witnesses and notes from several White House aides. The Justice Department responded it would also be willing to negotiate on the committee's document request so long as the House called off its contempt vote against Barr.

While the Judiciary Committee still sees the resolution as part of the civil contempt process to enforce subpoenas through the courts, the Justice Department only considers it an effort to enforce subpoenas, and not contempt, according to a Justice Department official.

Nadler noted that Tuesday's vote included language authorizing court action against McGahn, in addition to Barr. He said that as long as the Justice Department "proceeds in good faith," there would be no further steps taken against Barr, but added: "If important information is held back, then we will have no choice but to enforce our subpoena in court and consider other remedies."

Rep. Doug Collins of Georgia, the top Republican on the Judiciary Committee, praised the agreement while suggesting the House should call off its floor vote on Tuesday.

"In light of today's agreement from the Justice Department, it's logical to ask: Is the chairman prepared to rescind his baseless recommendation to hold the attorney general in contempt, or do House Democrats still plan to green light lawsuits against the attorney general and former White House counsel tomorrow?" Collins said in a statement.