Because of the boycott of the January elections, only 17 Sunnis have seats in the 275-seat national assembly.
"That is the problem that Sunnis face now,'' said Tariq Hashimi, secretary general of the Iraqi Islamic Party. "We are not represented in the assembly. How can we participate in writing a constitution?''
The new government is charged with writing a constitution by Aug. 15. A national vote on the constitution would follow, leading to the election of a new, full-term government.
Only one of the 55 members of the committee charged with drafting the constitution is Sunni. Samarrai said assembly authorities had agreed to add more Sunnis to the process and had asked Sunni leaders to recommend 10 or more nominees.
Broad Sunni participation in the next elections will be conditional on a constitution that guarantees the rights of all Iraqis, Samarrai and other Sunni officials said. If the constitution is satisfactory, "We'll not miss the chance again. We'll not make the same mistake'' of sitting out elections, Samarrai said.
Emotions at the conference peaked when speakers called for the resignation of Iraq's interior minister, Bayan Jabr, a Shiite, as head of the police forces.
In a news conference later, Jabr rejected the call for his resignation. "No one has the right to fire, or force to resign, except the National Assembly,'' he said. "Those who have no voice should not demand to be listened to.''
A U.S. official in Baghdad said Jabr's appointment and the recent killings of clerics may have prodded Sunnis to participate in the political process.
"My sense is they have peered over the edge, and decided that's really not where they want to go,'' the official said on condition of anonymity, referring to growing sectarian tensions.
No single step will end the insurgency, the official said. "I do not believe it is going to happen in a big bang,'' he told reporters.
Conference organizers said former Iraqi military officers also attended. Hussein-era military officers are believed to be among the leaders of homegrown resistance to the U.S. military presence and to the Iraqi government it supports.
In addition to Sunnis, foreign fighters including Abu Musab Zarqawi, a Jordanian, have played a lethal role in the insurgency. A statement attributed to Zarqawi that was released on the Internet last week defended killing innocent Muslims in the interest of harming Americans and Shiites.
Hareth Dhari, a senior member of the Association of Muslim Scholars and a proponent of the Sunni election boycott, did not attend the conference, but his son was present.
A representative of the Supreme Council for the Islamic Revolution in Iraq, one of the two Shiite political parties leading the country, also attended the conference.
Another influential Shiite leader, the radical cleric Moqtada Sadr, said in an interview on al-Arabiya television that he was responsible for pushing the Sunni leaders into action, with approval from Shiite leaders.
"I tried to end the strife,'' Sadr said in rare public comments since leading an armed revolt against U.S. troops last year. "They both agreed, and both are willing to take the advice and avoid disagreement, because Iraq needs unity now.''
The National Dialogue Council, a Sunni group that took a lead role in negotiating Sunni posts in the new Shiite-led cabinet, also did not send a representative to the conference.
Delegates at the conference prevented a representative of a Sunni who has joined the governing Shiite-led coalition from speaking at the meeting. "No to those who sold out Sunnis,'' delegates shouted, then chanting, "Allahu Akbar,'' or "God is Great" until the man stopped speaking and stepped back from the podium.
Separately Saturday, the U.S. official accused Syria of harboring supporters of the insurgency in Iraq.
"There are people inside Syria, known to the Syrian government, who are encouraging acts'' in the insurgency, he said. "The Syrian government knows what it needs to do.''
A U.S. offensive this month in western Iraq involving more than 1,000 Marines targeted foreign fighters believed to have infiltrated the country from Syria. Secretary of State Condoleezza Rice and other officials have expressed concern about Syrian influence in Iraq.
Sunnis, Americans and others have also expressed concern about Iranian influence in the new Iraq. The official who spoke Saturday, however, had less harsh words for Iraq's eastern neighbor.
"I think Iraq needs good relations with Iran," the official said. "Iraq does not need another foreign war. Over time, Iraq's economy would benefit -- they have a self-interest in having good relations with Iran."
Special correspondents Omar Fekeiki and Khalid Saffar contributed to this report.
