WASHINGTON (CNN) -- Attorney General Eric Holder agreed Monday to meet with the Republican chairman of the House Oversight Committee, but sought to add top congressional Democrats in the latest step of a showdown over the panel's push for more Department of Justice documents on the botched Fast and Furious gun-running sting operation.

Rep. Darrell Issa of California, the chairman of the House committee, has scheduled a vote later this week on a measure citing Holder for contempt for failing to turn over the documents he seeks.

However, Issa offered Friday to postpone the vote if Holder followed through on an earlier pledge to turn over some of the documents.

Issa also agreed last week to a meeting on the issue, as requested earlier by Holder, but made clear he wanted the documents ahead of time and also wanted Sen. Charles Grassley of Iowa -- the ranking Republican on the Senate Judiciary Committee and a leading critic of Holder -- to take part.

In a letter Monday responding to Issa, Holder agreed to a meeting on Tuesday. However, Holder said the meeting should also include the chairman of the Senate Judiciary Committee -- Pat Leahy of Vermont -- and the ranking Democrat on Issa's panel -- Rep. Elijah Cummings of Maryland.

Holder also indicated he would turn over the documents at the meeting, rather than ahead of time.

His letter said the purpose of the meeting would be to reach an agreement that would avoid a "constitutional confrontation" -- a reference to the committee's planned vote on the contempt measure.

Justice officials and Issa's committee have been battling for months over the materials sought by the chairman, with Issa accusing the attorney general of stonewalling the investigation into Fast and Furious.

The Justice Department says it already has handed over more than 7,000 pages of records to House investigators, and says the remaining material Issa wants could jeopardize criminal prosecutions.

The Bureau of Alcohol, Tobacco, Firearms and Explosives launched Operation Fast and Furious out of Arizona to track weapons purchases by Mexican drug cartels.

However, it lost track of more than 1,000 firearms that the agency had allowed straw buyers to carry across the border, and two of the lost weapons turned up at the scene of the killing of a U.S. Border Patrol agent.

Issa and Grassley have accused Holder and other top Justice Department officials of withholding requested documents and misleading them about when they first learned of the program.

Holder fended off a call for his resignation last week at a Senate Judiciary Committee hearing, where Sen. John Cornyn, R-Texas, accused him of misleading Congress over the Fast and Furious program and other misdeeds.

Holder called Cornyn's complaint "almost breathtaking in its inaccuracy" and added, "I don't have any intention of resigning."

CNN's Tom Cohen and Ted Barrett contributed to this report.