The Sunni minority is believed to be the backbone of the anti-US and anti-interim government uprising and many blame the impasse in forming a new government for a resurgence in violence.
The development comes as US Secretary of State Condoleezza Rice, joined by other top US officials, tries to persuade politicians from the Shia majority and their Kurdish allies to wrap up negotiations to form a new government.
As leaders of Iraq's main Shia, Sunni and Kurdish factions continued their disputes, Prime Minister-designate Ibrahim al-Jafari again put off his long-promised cabinet announcement.
The National Dialogue Council, a coalition of 10 Sunni factions, initially requested 16 cabinet seats.
It submitted a list of candidates on Sunday that included former members of Saddam Hussein's Baath Party, said Jawad al-Maliki, a senior member of al-Jafari's United Iraqi Alliance.
Al-Jafari (C) has once again
delayed announcing the cabinet
But when that was rejected, they dropped the demand, he added.
Alliance members, who control 148 seats in the 275-member National Assembly, refuse to give any top posts to members of the party they believe carried out Hussein's suppression of the Shia and Kurds.
The issue is just one of many obstacles that have bogged down negotiations since the 30 January parliamentary elections. Most Sunnis either boycotted the vote, citing the presence of foreign troops as an obstacle or stayed away for fear of being attacked.
Al-Jafari could present his cabinet to parliament on Tuesday, some alliance members said. But such forecasts have repeatedly been proven wrong.
The prime minister-designate has had to balance demands by his predecessor, Iyad Allawi, for at least four ministries for his party, including a senior government post and a deputy premiership.
Much of the discussion has focused on the Defence Ministry, which all agree should go to a Sunni, but which Allawi has argued should go to someone from his Iraqi List party.
US, EU reaction
Rice telephoned Masud Barzani, head of the Kurdish Democratic Party, on Friday to ask him to finish forming a government as soon as possible, two State Department officials said on Monday.
The US signalled its impatience with the failure of Iraqi leaders to complete the formation of a new government.
"I think everybody believes that the Iraqi people now deserve a government, given that they took [a] risk to vote," Rice said.
Rice says it is time that Iraq
formed its new government
"We've had opportunities to represent those views to a number of Iraqi leaders," she said from President George Bush's ranch in Texas. "And we're going to continue to say that it is important to keep momentum in the political process."
US officials had previously kept a low profile on the issue.
An ABC News/Washington Post poll shows Americans are pessimistic about Iraq, with 60% saying they are not confident it will have a stable, democratic government in a year.
The European Union, which wants to co-host an Iraq conference with the US in late June, also called on Iraqi leaders to speed up efforts to form a government.
EU external relations commissioner Benita Ferrero-Waldner urged "all sides to really form this government".
A Task Force Liberty Soldier was killed in a vehicle accident near Muqdadiya at 6.30am on Tuesday.
The cause of the accident is under investigation.
Meanwhile, three roadside bombs aimed at US military convoys exploded in the capital on Monday, including one that killed an American soldier, said Lieutenant-Colonel Clifford Kent of the US 3rd Infantry Division.
According to the Pentagon, 1573 members of the US military have died since the beginning of the Iraq war in March 2003.
An American soldier was killed in
The US military said a car bomb exploded on Monday in Ramadi, 115km west of Baghdad, wounding two civilians, and a 20-year-old Iraqi died at a US military hospital of injuries he suffered two weeks ago while attacking US-led forces.
Fighters also launched two attacks on Monday aimed at Iraq's oil industry in the north, setting fire to pumps near Kirkuk and opening fire on police guarding a convoy of tanker trucks.
Two policemen were wounded and three fighters arrested in a gun battle over the convoy, police said.