Mahmud Uthman, a Kurdish member of parliament, has confirmed that the president, Jalal Talabani, is continuing his efforts to bring anti-US fighters to the negotiation table.
In an interview with Radio Sawa, an Arabic radio station broadcast from Washington and funded by the US government, he said that seven armed groups had given conditional agreement.
The groups demanded that the plan include a recognition of "Iraqi resistance" and a US withdrawal timetable.
Uthman said that 11 other groups including al-Qaeda in Iraq and the al-Qaeda-linked Ansar al-Islam had rejected the plan.
Major armed groups such as Kataib Thawrat al-Eshrin (Brigades of 1920 Revolution) rejected the plan of the prime minister, Nuri al-Maliki, in a statement posted online, rejecting earlier statements by politicians that the brigades had approved the plan.
The brigades mainly consist of former Iraqi army members.
The statement said the plan did not deal with the withdrawal of the "occupation forces", did not recognise resistance and did not mention the issue of death squads and militias.
Tribal leaders from western Iraq, the stronghold of Iraq's revolt against US-led forces and the Iraqi government, have backed the conditional agreement of some Iraqi groups.
Sheikh Fahran al-Sidaid told the London-based Arabic newspaper al-Hayat that tribal leaders in western Iraq want to hold face-to-face talks with the government.
"The talks would be in parallel to put pressure on the armed groups, if the government deals seriously with the militias issue and shows clear understanding of the difference between resistance and terrorism," he said.
Al-Maliki's plan, disclosed on Sunday, was thought to have denied amnesty to any fighter who had killed American forces.
In the first tangible measure after the reconciliation plan was announced on Sunday, the council of ministers said government employees who had been detained and recently released would be reinstated to their jobs.
The ministers said freed students would be allowed to return to school to take their final exams and would not be failed for the 2005-2006 school year despite the time missed.
More than 400 detainees were
freed from US prisons
The measures were decided at the council's session on June 21 "to pave the way for the prime minister's reconciliation initiative", according to a statement released on Monday.
It said the benefits could only be enjoyed once by former detainees and would not apply if somebody was arrested again.
The justice ministry, meanwhile, said 453 more detainees were released from US detention centres across Iraq, part of al-Maliki's plans to free 2,500 by the end of the month as a goodwill gesture.
Sunni Endowment support
In another boost for the Shia prime minister's reconciliation proposal, Ahmed Abdul Ghafour al-Samaraie, head of the governmental Sunni Endowment, offered his support to the plan.
But he called on the government to move quickly to fill in the details of the plan and said it should include the disbanding of armed militias, as well as the release of all prisoners who had not been convicted.
Al-Samaraie welcomed the
"We bless this initiative," he said.
"We see a glimpse of hope out of this plan, but at the same time we are noticing that some people are pushing the armed groups to attack some areas in Baghdad, spreading terror and chaos in the city in order to make this plan a failure.
"Thus, the government is required to take decisive actions so that the citizens feel that the state is a real protector.
"We think that the first step to be taken regarding this plan is to disband armed militias."
Shia-led militias have been blamed for random detentions and torture.