Iraqi Shiite Muslims are leading the call for early direct elections, rather than caucus-style elections in 2005 under the U.S. plan announced in November.
The United Nations is expected to send the team sometime this month, but reportedly not before the end of the Muslim Eid al-Adha holiday on Friday.
"I hope this team I'm sending in will be able to play a role, getting the Iraqis to understand that if they could come to some consensus and some agreement on how to establish [a provisional] government, they're halfway there," Annan said during a visit with President Bush in Washington, according to the Associated Press.
Hassan al-Amiri, secretary-general of the Badr organization, the military wing of Iraq's main Shiite political group, said in an interview with Reuters on Wednesday that even imperfect elections should be allowed to proceed.
The United States has said that since there are no voter rolls, Iraq's infrastructure is still being rebuilt and security is precarious, elections cannot be held before the end of June.
But Amiri said he does not believe those factors should delay elections.
"Over 90 percent of Iraq is safe. The south is safe, the north is relatively safe," he said. "The Iraqis are protecting hospitals, schools and other institutions. They can protect polling centers."
Iraq Shiite clerics say holding elections before the June 30 transfer of power would avoid the United States appointing leaders in the interim, and direct elections would ensure that Iraq's 60 percent Shiite majority is given proportional representation in the new government.
Under the U.S. plan, the Iraqi Governing Council would choose small groups of people from each of the country's 18 regions to elect a member to the new government, thereby ensuring the representation of Iraq's many ethnic and religious groups, the United States has said.
Even if the U.N. team does not support the demand for early elections, the Shiites could still press their case through civil disobedience and mass demonstrations, Amiri told Reuters.