A statement issued at the end of the meeting at Baghdad's Umm al-Qura mosque, the headquarters of Iraq's leading Sunni body, called for "an internationally guaranteed timetable for the withdrawal of foreign troops".
The meeting involved a representative of the Association for Muslim Scholars, an Arab nationalist, a former member of ousted president Saddam Hussein's Baath party and a representative of radical Shia cleric Muqtada al-Sadr.
None of those present took part in the 30 January election mostly because they objected to a vote being held under what they call "foreign occupation".
End to sectarianism
The group also listed "an end to handing out political posts based on religious, racial or ethnic criteria, (and) recognition of the people's right to resist" the occupation as their conditions for taking part in "national reconciliation and drawing up the constitution".
Shia and Kurdish leaders who emerged victorious from the vote have admitted the necessity of bringing in marginalised groups to help draw up the constitution in order for the country to move forward.
The group stressed their "rejection of terrorist acts against innocent Iraqis, infrastructure and places of worship".
Five Iraqis were killed in
different attacks on Tuesday
"The administration that will emerge from the elections must not have the right to agree international treaties which could harm Iraq's sovereignty and independence, nor its natural resources," said the statement.
Participants said the incoming government would be "illegitimate", adding that election day had seen "fraud" and a low level of participation.
They stressed the necessity of "adopting democracy as a means of rotating power ... respecting the Arab and Muslim identity of Iraq, (and freeing) political prisoners, especially women."
Elsewhere five Iraqis were killed and nine others wounded in a string of insurgent attacks across the country, security sources said Tuesday.
Two soldiers were killed and another wounded when a bomb exploded near the restive Sunni town of Dhuluiyah, north of Baghdad, Captain Asad Amjad said.
"The blast went off at 9.00 am as an army patrol drove by," the officer said.
Near the town of Balad, further north, the body of an executed soldier was pulled out of the Tigris river, a police source said. It was not clear when and in what circumstances he was killed.
Five Iraqis, including a child and a soldier, were also wounded Tuesday in a blast in Abu Farraj, near Saddam Hussein's home town of Tikrit, police said.
In Baghdad, a policeman and a member of the civil aviation administration were shot dead late Monday, police said.
Three other policemen were also wounded in a mortar attack in the capital.