About 250 members of Iraq's political and ethnic groupings on Monday met in Baghdad and agreed to hold a national conference within four weeks to choose an interim government.
Many of the delegates hailed the agreement as a breakthrough for democracy.
"This is the start of democracy. Discussions were serious and deep. It is a long and difficult road but we shall cross it," said one delegate, Hatem Mokhless.
The delegates told retired US general Jay Garner, who is overseeing the reconstruction of Iraq, that they were grateful to Washington for removing Saddam Hussein, but now wanted to run their own affairs.
Those in attendance included clerics from the Shi'ite majority and from the traditionally dominant Sunni Muslims, as well as Kurds from the northern mountains.
Arab tribal chiefs in robes and headdresses mingled with urban professionals in Western-style suits.
Some delegates said splits emerged between returned Iraqi exiles and those who had lived through the Saddam years.
Most former exiles wanted a lesser US role, arguing that only Iraqis should rule the country, while those who had remained at home said they wanted more US supervision because they did not trust the exiles.
In Dearborn, Michigan, on Monday, US President George W Bush told a large number of Arab and Muslim immigrants: "America has no intention of imposing our form of government or our culture [on Iraq], yet we will ensure that all Iraqis have a voice in the new government and all citizens have their rights protected.
"Whether you are Sunni or Shia or Kurd or Chaldean or Assyrian or Turkmen or Christian or Jew or Muslim, no matter what your faith, freedom is god's gift to every person in every nation."
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