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

The precise scope, volume or usefulness of the material was not immediately clear, but the chairman of the House Judiciary Committee, Representative Jerrold Nadler of New York, said it would include “interview notes, firsthand accounts of misconduct and other critical evidence” collected by Mr. Mueller from the White House and former officials.

The deal appeared to provide a rationale for House Democrats’ choice, announced last week, to back away from threats to hold Attorney General William P. Barr in contempt of Congress for defying a subpoena for the materials in question. Out of an abundance of caution, the House still planned move forward with a Tuesday vote to empower the Judiciary Committee to take Mr. Barr and other noncompliant witnesses to court to fully enforce their subpoenas if necessary.

And another panel, the House Oversight and Reform Committee, is to vote on Wednesday to recommend that the House hold Mr. Barr and Commerce Secretary Wilbur Ross in contempt for defying subpoenas in a different case related to the Trump administration’s addition of a citizenship question on the 2020 census.