In a letter this week, the Justice Department had signaled that it was willing to renew negotiations with the Democrats over access to unredacted text of the Mueller report and all of the material the special counsel’s investigators collected if Democrats would nullify the Judiciary Committee’s recommendation and remove “any threat of an imminent vote by the House of Representatives to hold the attorney general in contempt.”

Representative Jerrold Nadler of New York, the Judiciary Committee chairman, rejected the department’s demand but said he would be willing to talk “without conditions.” But by declining to hold Mr. Barr in criminal contempt of Congress for now, Democrats may be leaving room to still reach a deal with the Justice Department while still allowing lawmakers to go on the record with their discontent and readying themselves for a court battle. Nor did they rule out pursuing criminal contempt in the future.

Instead, Democrats have drafted a measure meant to expedite their path to the courts to try to enforce the House’s demands for documents and testimony to further multiple House investigations, including one into possible obstruction of justice and abuse of power by President Trump.

“We will not allow this president and his administration to turn a blind eye to the rule of law,” said Representative Jim McGovern of Massachusetts, the Rules Committee chairman. He added, “This resolution will allow Congress to hold the president accountable while the Democratic majority continues delivering on issues like health care and jobs.”

Democratic leaders are trying to find a path to hold Mr. Trump accountable for the misdeeds detailed in the Mueller report while holding at bay the growing forces calling for the president’s impeachment. Still, the omission of language about contempt in the Rules Committee resolution may complicate that effort if liberal lawmakers see it as insufficiently punitive.