London ? Iraqi exiles declared they wanted to build a “new Iraq” and agreed Tuesday on a power-sharing plan that for the first time recognizes the political clout of Shiite Muslims who are a majority in a nation long controlled by Sunni Muslims such as Saddam Hussein.

The agreement by Iraq’s usually fractious opposition groups resulted from a heated London conference aimed at mapping out Iraq’s political future if Saddam is ousted, and finding accord among exiles divided along ethnic, political and religious lines.

Aspirations were high. Delegates settled on the size of a committee that could form the basis of a post-Saddam transitional government, and plan to reconvene Jan. 15 to decide the committee’s leadership. Ahmed Chalabi, whose Iraqi National Congress was one of the six main factions at the conference, said that meeting would take place in northern Iraq, their enemy’s back yard.

Northern Iraq slipped from the Iraqi president’s control after the 1991 Gulf War and now is run — under the protection of U.S. and British war planes — by two Kurdish groups that took part in the meeting that ended Tuesday.

Negotiations in London were so tough that delegates retreated into a closed session to hammer out details after having a closing news conference complete with ringing declarations in support of reconciliation and tolerance. The conference, which had been scheduled to end Sunday after three days, lasted two days longer as delegates fought over the committee’s size and composition.

Hours after their news conference, organizers released a list of the committee’s 65 members. Shiites, largely denied political power under Saddam and his predecessors, held nearly half the seats at 32.

The list included key leaders such as Chalabi, whose Iraqi National Congress is an umbrella for opposition groups; Iyad Allawi, leader of another umbrella group, the Iraqi National Accord; and Abdelaziz al-Hakim, whose brother Ayatollah Mohammed Baqir al-Hakim heads the Iran-based Shiite group the Supreme Council for the Islamic Revolution in Iraq.

Three women, all Shiites active in independent anti-Saddam groups, got places. Among them was Safiya al-Soheil, whose father, Talib al-Soheil, helped plot a 1993 coup attempt against Saddam before fleeing with his family. He was killed in 1995 in Lebanon, apparently by Saddam’s agents. She has campaigned for Saddam to be punished for crimes against the Iraqi people.

Conference delegates earlier agreed on a list of 49 current Iraqi regime officials — including Saddam and his two sons — who should face war crimes trials. Other officials would be granted amnesty.

A statement issued at the end of the conference suggested a three-man Sovereign Council to lead a transitional government. The council would be modeled on one established after a 1958 Iraqi coup that included an Arab Sunni, a Shiite and a Kurd.

Other proposals in the statement included having elections within two years and separating legislative, executive and judicial powers. It also declared Islam the state religion and basis of laws. Saddam’s Baath party espouses secularism, but elements of Iraqi society are religiously conservative.