The council agreed on Tuesday that the presidency of the self-rule body would rotate among nine of its members.
A source at the council said the decision, which was taken after a six-hour meeting, reflected the members' "wish to share responsibilities in this sensitive period".
Choosing a leader was supposed to be one of the first tasks of the council, which held its first meeting on July 13 and is seen in Washington as a first step towards democratic government in Iraq.
But members took more than two weeks to decide.
Hoshiyar Zebari, political adviser to Masoud Barzani, leader of the Kurdish Democratic Party, said: "We discussed a number of proposals in a civilised and free way and we all agreed on this compromise formula."
Zebari said the rotation period and order would be decided in the coming days.
"The council may resort to alphabetical order or to voting to decide who will lead it first and the period may be one month or two," he said.
"We discussed a number of proposals in a civilised and free way and we all agreed on this compromise formula"
Kurdish Democratic Party
The nine members include Iraqi National Congress head Ahmad Chalabi; the leaders of the two Kurdish parties; Iyad Allawi of the Iraqi National Accord; Abd al-Aziz al-Hakim of the Shia Supreme Council for the Islamic Revolution in Iraq; Ibrahim Jaafari of the Da'wa Party; and Muhsin Abdul Hameed of the Iraqi Islamic Party.
Adnan Pachachi, a former foreign minister who has returned from exile, and Muhammad Bahr al-Uloum, an Islamic scholar, are also on the list.
US retains control
The Council has the power to name and dismiss ministers, approve the 2004 budget and decide policy on economic and electoral reform.
It is also supposed to work out a new constitution leading to an elected, internationally-recognised Iraqi government able to take over from the council and end the military occupation.
However, final control of Iraq still rests with the US occupation-power administrator in Baghdad, Paul Bremer.