The deadline for completing the draft is 15 August, and the charter will be submitted to the electorate for approval two months later.
Speaking to reporters on Tuesday, President Jalal Talabani, a Kurd, said the committee was making good progress "but there are some Arab brothers" who "have some reservations that are being taken into consideration".
"If we can reach an agreement with them, I believe the constitution can be ready by the end of the month," he said.
Talabani did not identify the critics but he was clearly referring to Sunni Arabs who want a strong statement affirming Iraq's Arab identity and who oppose some definitions of federalism supported by the Kurds and some Shia Muslims.
Those are among the major hurdles standing in the way of completing the constitution.
Former prime minister Iyad Allawi, a secular Shia, said he supported using the interim constitution, approved before Iraq regained sovereignty from the US-led occupation authority.
"As soon as the referendum on it [the constitution] is finished, Iraq will have stability"
former interim prime minister
Some Shia oppose the interim charter's limitations on the role of Muslim law as the basis of the legal code. Some Sunnis oppose autonomy guarantees given to the Kurds as a threat to national unity.
"Concerning the constitution, we are in agreement with the national and Kurdish forces that the interim constitution be the basis for the Iraqi constitution," Allawi said.
"I believe that will allow Iraq to have the constitution. As soon as the referendum on it is finished, Iraq will have stability."