In a meeting with a group of Sunni and Shiite leaders, the cleric, Ayatollah Ali al-Sistani, outlined a proposal that would scrap the system used in the January election, according to a secular Shiite political leader, Abdul Aziz al-Yasiri, who was at the meeting. The election had a huge turnout by Shiites and Kurds but was mostly boycotted by Sunni Arabs.

Such a change would need to be written into Iraq's new constitution, which parliamentarians are drafting for an Aug. 15 deadline. Although there has been little public talk about what form elections might take under the constitution, Ayatollah Sistani has been highly influential in Iraq's nascent political system.

Under the proposal, voters in national elections would select leaders from each of the 19 provinces instead of choosing from a single country-wide list, as they did in January. The new system would essentially set aside a number of seats for Sunnis roughly proportionate to their numbers in the population, ensuring that no matter how low the Sunni turnout, they would be guaranteed seats.

Sunni Arabs welcomed news of the suggestion. "This should have been done from the beginning," said Saleh Mutlak, a member of the National Dialogue Council, a Sunni Arab political group that has pressed for a more active role in politics. "That election was wrong."

The January elections ended in a decisive victory for Shiite Arabs and Kurds, leaving just 17 seats for Sunni Arabs in the 275-seat National Assembly. Voting in largely Sunni areas was extremely low, depressed by threats from insurgent groups who opposed the election.

Iraqi and American officials say feelings of disenfranchisement among the Sunni Arabs, who ruled Iraq for decades, may be fueling the insurgency. The violence has cut deeply into Iraqi society, with about 1,200 Iraqis and more than 75 American soldiers killed in the past two months. The attacks have taken on increasingly sectarian overtones, raising fears that Iraq could be headed toward civil war.

At least 10 Iraqis were killed and more than 36 wounded in attacks across Iraq in the past 24 hours.

A car bomb exploded late Sunday outside a barbershop in the New Baghdad district of the capital, killing the shop owner, a customer and a 4-year-old boy, an Interior Ministry official said. Barbershops have been singled out by Islamic attackers because they offer Western-style shaves and haircuts. On Monday, at least 4 Iraqis were killed and 29 wounded when a car bomb exploded outside a restaurant in the same neighborhood.

Also on Monday, two American soldiers were killed when their Apache helicopter crashed about 11 a.m. near Taiji, a large air base northwest of Baghdad, said Master Sgt. Greg Kaufman, a military spokesman. It was the third loss of an American helicopter in about a month.

The military did not say what caused the crash. The Associated Press quoted an Iraqi witness as saying a rocket had hit it, and other witnesses heard heavy gunfire. Sergeant Kaufman could not confirm any of the details.

Another American was killed Monday in central Baghdad while he helped Iraqi policemen investigate a burning car, the military said.

In a Pentagon briefing on Monday, the top American commander in Iraq, Gen. George W. Casey Jr., confirmed that American and Iraqi officials had been meeting with Sunni leaders in Iraq in hopes of defusing the insurgency and drawing their followers into the political process. General Casey denied that the meetings constituted negotiations, and said he was unaware of any direct contacts with insurgent fighters.

"They're discussions primarily aimed at bringing these Sunni leaders and the people they represent into the political process," he said at a briefing with Defense Secretary Donald H. Rumsfeld. "But to characterize them as negotiations with insurgents about stopping the insurgency, we're not quite there yet."

Both General Casey and Mr. Rumsfeld have said there have not been any contacts with foreign fighters like the Jordanian militant Abu Musab al-Zarqawi, who is believed to be responsible for some of the most deadly suicide attacks in Iraq.

The statements by Ayatollah Sistani are the latest foray into Iraqi politics by the Shiite leader. Pressure from him was a major factor in establishing an accelerated timetable for the elections in January. That pace, however, largely dictated the election's countrywide system, because United Nations organizers considered it the simplest and quickest way to organize the vote.

When United Nations officials met with the ayatollah in March, he chastised them for choosing the system, and said he favored setting assembly seats aside district by district, a preference he reiterated Monday. Mr. Yasiri, the Shiite politician, said Ayatollah Sistani had characterized the January election as flawed.

In the past, the ayatollah has reserved his efforts to pushing for measures, like nationwide elections, that were likely to enhance the power of Iraq's Shiite majority. His endorsement of a new voting system seemed to be made out of concern for the delicacy of the current political situation here.

"He said there were a lot of mistakes," Mr. Yasiri said. "He said this election must be different than the old one. He said we prefer that all the people share in it."

In other news, Iraq's foreign minister under Saddam Hussein, Tariq Aziz, in a videotape of his interrogation that was released Monday and described by Agence France-Presse, said Mr. Hussein had personally ordered the crackdown on a Shiite uprising in 1991 without consulting top aides. The testimony could help prosecutors build a case against Mr. Hussein for his trial.

David S. Cloud contributed reporting from Washington for this article.