Iraq's Prime Minister Nouri Maliki has said a number of insurgent groups have responded positively to his national reconciliation plan.
Mr Maliki said some militants were ready to lay down arms
The plan, which Mr Maliki presented to parliament on Sunday, aims to stem sectarian violence by offering an amnesty to some insurgents.
Mr Maliki welcomed the response and said he would talk to anyone not involved in bloodshed or crimes.
Hardcore Islamist militants have already denounced the plan.
Mr Maliki said he and others in the government had been contacted directly by many of those who had been involved in the so-called resistance or other military activities.
They had said they were ready to join the political process and lay down their arms, Mr Maliki said.
According to Associated Press news agency, 11 Sunni insurgent groups have offered to stop attacks on US-led forces if there is a two-year timetable for foreign forces to leave.
Mr Maliki did not reject the demand outright but said it would prove difficult to hand over all security to Iraqis by then.
There are thought to be about 25 identified insurgent groups in Iraq.
Naseer al-Ani, of the largest Sunni political group, said if the plan were properly initiated "70% of the insurgent groups will respond positively".
However, the BBC's Jim Muir in Baghdad says much will depend on how seriously the government follows up on issues of Sunni concern, such as curbing the powerful Shia militias, blamed for sectarian violence, and releasing detainees not convicted of serious crimes.
Under Mr Maliki's plan a new commission will be set up to oversee the reconciliation process, with branches in all of Iraq's provinces.
Who is eligible for amnesty will remain a difficult subject for discussion, particularly for the US which has lost hundreds to insurgent attacks.