Appearing before parliament on Monday, Chairman Humam Hammoudi said if political leaders met this week to resolve the differences "on 15 August, we will be able to conclude the constitution."
Hammoudi added one condition: "The leaders of the bloc meet on 5 August, and on 12 August we receive the results of their discussion. If there are any points of disagreement among the leaders, they will be brought forward to the National Assembly in order for them to solve it."
Hammoudi told parliament that he had recommended that the commission formally ask the National Assembly for more time after the members faced a deadlock on such issues as the role of Islam, federalism and distribution of the national wealth.
But the US authorities ratcheted up pressure on Sunday to stick by the deadline, which Washington considers essential to maintain political momentum, undermine the insurgency and pave the way for the Americans and their partners to draw down troops next year.
After meeting US Ambassador Zalmay Khalilzad, President Jalal Talabani said on Sunday that all efforts had to stick to the timetable and finish the charter by 15 August.
Intense meetings took place late into the night to find a way out of the impasse.
The interim constitution, which forms the legal framework for all current Iraqi government activities, states that parliament must approve the draft by 15 August, not simply that the committee produce the document.
US has increased the pressure on
Iraq to keep on schedule
Once the document receives parliamentary approval, the charter goes to the voters for approval in a referendum in mid-October.
Members of the drafting committee have been warning for weeks that although 90% of the document was completed, the 71 members could not agree on a handful of key issues, including federalism, the role of Islam, the distribution of national wealth and the name of the country.
The Americans fear that any delay in the constitutional process would serve as an opening to insurgents and widen the gulf among ethnic and religious groups.
Women from different Iraqi rights groups met on Monday to issue a list of demands they believe will guarantee women's rights in the country's new constitution.
The informal group issued a six-point statement demanding that Islamic law, or Sharia, is not one of the sources of the constitution; that Iraq should abide by all international treaties concerning human rights and the rights of women and children; and that all Iraqi men and women have equal legal rights.
"On 15 August, we will be able to conclude the constitution"
Chairman Humam Hammoudi
The statement also calls for female representation in the three branches of government and in other decision-making positions to be no less than 25%.
The role of Islam remains an important stumbling block in completing Iraq's new constitution.
An early draft published in the al-Sabaah newspaper last month suggested Islam was to be the official religion of the State and the main source of legislation. Some MPs want this amended to say Islam is only a source of the constitution.
The text is supported by the conservative Shia majority in Iraq's parliament. It is, however, still under discussion by a parliamentary committee and subject to revision.
Participants at the Baghdad meeting included Women's Affairs Minister Azhar al-Sheikli, Ahlam Lafta, a university law professor, Iraq's ambassador to Egypt Safia al-Sihail, and former environment minister Pascale Warda.