"We propose forming a committee outside parliament with representatives from across Iraq," Nasser al-Ani, a spokesman for the Sunni Arab Iraq Islamic Party, told AFP on Monday.
"We want our Shiite partners to give us an expanded role in this process."
New Prime Minister Ibrahim Jaafari had pledged on Sunday to get more Sunnis involved in drafting the constitution after meeting with Rice during her surprise visit to Iraq.
Parliament has just set up a committee to draft the constitution by 15 August.
The draft is then to be put to a nationwide referendum by 15 October under a deadline set by the US-inspired transitional administrative aaw, currently governing Iraq.
Sunni Arabs are under-represented
in Iraq's new parliament
Favoured under former president Saddam Hussein, Sunni Arabs, who account for about 20% of the population, provide the backbone of the ongoing fighting that has claimed more than 400 lives since the start of the month alone.
Shiite and Kurdish leaders, who swept to power in the landmark January elections, believe that involving Sunni Arabs in the new administration is essential to undermining support for the insurgents.
But many of their own constituents, who suffered under Saddam, want revenge and have called for purging the administration of leading - often Sunni - members of the former ruling Baath party.
Because many Sunni Arabs boycotted the country's 30 January election, they are currently under-represented with just 16 seats in the 275-member assembly.
Following weeks of protracted haggling, they were given nine of the 36 cabinet posts, including the powerful defence minister slot. But their lack of parliamentary representation has cost them dearly in getting a voice on parliament's constitutional committee.
The 55-member body includes just two Sunni Arabs. "The solution is to have a commission which includes members of parliament and people from outside the parliament," Hajem al-Hassani, the Sunni speaker of parliament suggested.
Qassem Daoud, a national security advisor to former prime minister Iyad Allawi and a Shiite member of the parliamentary constitutional committee agrees that an independent committee might be a good idea.
"It is necessary to create a sub-committee which would be a kind of national conference. That's the best solution," Daoud told AFP.
Selecting Sunni representative could still prove to be a problem,
US and Iraq government are not
ready to set a date for troop pull out
however, as can be deduced from a statement by the Association of Muslim Scholars, considered the most influential Sunni authority. The association has warned that it will take part only if a timetable is set for the withdrawal of foreign forces.
American and Iraq authorities have refused to set such a deadline.
Drafting a constitution in time to meet the August deadline is likely to prove "an intense challenge", according to Nicholas Haysom, head of a United Nations team on hand to advise Iraqis.
Some experts have suggested the current transitional law should serve as a template for the new constitution.
But the document does not address some of the big issues, including the role of Islam, rights for women or how much independence should be given to the three northern Kurdish provinces.
"Adopting the text (of the constitution) in a referendum..will be more difficult"
A member of the consitution commission
"To write a constitution isn't the problem," said Yonnadam Kanna, a member of the parliamentary commission and chief of the Assyrian Democratic Movement.
"Adopting the text in a referendum, on the other hand, will be more difficult."
The draft constitution will fail if two-thirds of voters in any of Iraq's 18 provinces vote against it.