Kurdish lawmaker Mahmoud Othman linked the offer to al-Maliki's national reconciliation plan, involving amnesty for opposition fighters except those who had killed Iraqis, were involved in terrorism or committed crimes against humanity. Al-Maliki's plan, disclosed Sunday, was thought to have denied amnesty to any insurgent who had killed American forces, though the wording was vague.

The Mujahedeen Shura Council, the terrorist umbrella organization that includes al-Qaida in Iraq, rejected the reconciliation plan.

Shiite lawmaker Hassan al-Suneid, who first reported insurgent groups' gesture, said al-Maliki was considering a possible meeting with their leaders or contacts through intermediaries. Al-Suneid is a member of the political bureau of al-Maliki's Dawa Party.

The opening was confirmed by Othman, a close associate of President Jalal Talabani, who held face-to-face talks with seven insurgent organizations about two months ago. It was never clear which groups Talabani met with.

Al-Suneid gave the names of six of the seven organizations that approached the government Monday: the 1920 Revolution Brigades, the Mohammed Army, Abtal al-Iraq (Heroes of Iraq), the 9th of April Group, al- Fatah Brigades and the Brigades of the General Command of the Armed Forces.

"I expect that those groups are the same ones that have made contacts with President Talabani, and now they are widening the range of their contacts. Now they are more serious after the announcement of the (reconciliation) plan," al-Suneid told The Associated Press.

Othman was unable to name the groups or say whether they were the same ones Talibani had contacted. But he said they also sought talks with U.S. forces.

A meaningful truce with insurgents would make it much easier for the United States to withdraw troops from Iraq.