There is a political calculation, too: The constitution cannot be ratified if it is rejected by a two-thirds vote in three provinces, and Sunni Arab leaders believe they can thwart the ratification in provinces where they are the majority.
As part of their overtures, Sunni Arab and anti-occupation groups have insisted on a timetable for a U.S. withdrawal. U.S. and Iraqi officials, including Abdel-Mehdi, have argued against a timetable, saying it depends on the progress of Iraq's security forces, whose performance has been uneven at best.
Shiites at a Baghdad mosque celebrate last week's elections, seen by many Iraqis as a success, even though results are not yet known.
(Wathiq Khuzaie -- Getty Images)
"If we start fixing timetables by now, we will be in a difficult situation if we reach that time and we are not prepared," Abdel-Mehdi said in the interview at his home. "You can't announce it, and then say okay, I'll delay it for two months."
"It's better not to go trying to fix dates then to break those dates," he added.
Other demands among the opposition groups are for the release of prisoners captured by U.S. troops and their Iraqi allies and a halt to the policy of removing former Baath Party officials from state institutions.
That process is known in English as de-Baathification, although its Arabic terminology -- uprooting -- has alarmed those opposed to it. Abdel-Mehdi's party is among the proponents of intensifying the process, and officials from the Supreme Council have also suggested that its Shiite militia may play a greater role in Iraq's security forces and their fight with insurgents.
In the interview, though, Abdel-Mehdi struck a more conciliatory tone.
"People are more objective. They have less illusions," he said. "That's why I'm very happy to hear certain positive reactions coming from the (Association of Muslim Scholars). Their language is very positive."
With Sunni Arab support, particularly among parties opposed to the occupation, the government may have an easier time coping with the insurgency, which has stepped up attacks after a lull right after the Jan. 30 vote.
The Ansar al-Sunna Army said the seven National Guard members it killed were captured after an ambush Thursday near Abu Ghraib, west of Baghdad. Footage showed the men being shot as they kneeled with their eyes blindfolded.
The Islamic Army in Iraq said it killed three policemen captured in the same raid, although it did not post footage.
In the southern city of Basra, four Iraqi National Guard members were killed in a roadside bombing, news agencies reported, and gunmen assassinated a member of the Baghdad city council in a drive-by shooting. In Samarra, north of Baghdad, at least two Iraqi troops were killed by a blast that hit their patrol, the agencies reported.
The governor's office in Mosul announced Saturday that armed men kidnapped the brother of the police chief, who had vowed to crack down on insurgents. Gunmen overran a police station there Thursday, killing five policemen, officials said. Later, in the evening, the police chief said National Guard members freed his brother and arresting nine.
Staff writer Jackie Spinner in Sulaymaniyah and special correspondent Dlovan Brwari in Mosul contributed to this report.