A senior Western diplomat said the talks were a "moment of truth" for Nuri al-Maliki,
The prime minister met Jalal Talabani, the Iraqi president, a Kurd, and Adel Abdel Mehdi, the Shia vice-president, on Sunday to discuss the resignations.
Tareq al-Hashemi, who is
'Door open'
Al-Hashemi has been a regular critic of al-Maliki's alleged sectarian bias, but his Kurdish and Shia colleagues vowed to hold inclusive talks in the coming days.
On Wednesday, the National Concord Front,
After Sunday's meeting, al-Maliki said: "We agreed on making efforts in order to get the Concord Front back and to tackle what we are able to tackle, but not everything that they have demanded."
Abdel Mehdi said: "The prime minister's position is that he has refused to accept the resignations. This is a good thing and the door is open to discuss this topic."
Salim al-Jibouri, a senior member of parliament from the front, said the ministers would still quit, despite al-Maliki's decision not to accept their resignations.
He said: "We are insisting on our position. For us, the matter does not end with Maliki accepting or rejecting the resignations.
"We are talking about a program. The issue is if he accepts or refuses to accept our program."
The program refers to the front's lists of demands that include disbanding Shia fighters and giving the bloc a bigger say in security matters.
Saleem Abdullah, a spokesman for the front, said: "At the moment, we have no intention of changing our position on the resignations. It is not necessary for us to be a part of the government."
However, Abdulllah also said "the door to dialogue is open, even if we are outside the government".
Mortar attack
In a separate development, at least 13 people have been killed and 11 wounded by mortar bombs that struck a petrol station in eastern
Iraqi police said that nine mortar bombs landed in the area at dawn, destroying 13 cars as people lined up for fuel.
Several other mortar bombs landed at another petrol station in a nearby district, wounding six people.
As
Last Wednesday suicide bombers attacked two petrol stations, killing 70 people.
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Meanwhile, the
Haitham al-Badri, described by the military as "the al-Qaeda in
A military spokeswoman said: "He is also the terrorist mastermind responsible for the Golden Mosque bombing in
Major-General Abdel Karim Khalaf, interior ministry operations director, said that al-Badri was the head of the cell that carried out the February 2006 attack on the mosque, widely seen as the trigger for numerous sectarian revenge killings in
Last week, more than 1,000 Iraqi troops backed by US paratroopers launched an operation to expel al-Qaeda's Iraqi affiliate from
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Nuri al-Maliki,