The historic Loya Jirga, which was opened by former king Zahir Shah on 14 December, has formed a committee to unite the views of the 502 delegates, who have been debating the 160-article draft in 10 groups.
Later, the draft would be put to open vote, Safia Siddiqi, one of the four Loya Jirga deputy chairpersons, told reporters on Monday.
"We hope that by tomorrow (Tuesday) afternoon the reconciliation committee will finish its work but if not we still have time," she said.
The reconciliation committee includes Loya Jirga chairman Sibghat Allah Mujaddidi, his deputies, secretaries and three delegates from each of the 10 groups besides observers from the United Nations and the constitution drafting committee.
The convention will wind to a close on Thursday though officials have said that it could be extended if needed.
Deliberations at the meeting have mainly centred on the proposed presidential system of government, which has been opposed by a large number of delegates.
Many of them, including some powerful mujahidin, prefer a prime minister or a parliament with real powers to counter-balance sweeping presidential powers.
Karzai has made it clear that he
favours a presidential system
Uzbek leader and Deputy Defence Minister Abd al-Rashid Dustum told reporters that he favoured a parliamentary system.
"A parliamentary system is the right system," said Dustum, who was appointed to the Loya Jirga by President Hamid Karzai.
"The success of every government is based on the support of its people and people would support a government if their views are well reflected in the government."
Karzai has repeatedly said that he would only stand in polls scheduled for June 2004 if the Loya Jirga approves a strong presidential system.
However, opponents say that too much power in the hands of the president could widen the country's deep ethnic and factional divides.
Karzai, on the other hand, believes that a strong presidential system is needed as Afghanistan lacks mature political parties for a successful parliamentary democracy.
His spokesman denied alleged interference by the government to bolster support for the proposed presidential system.
"There has not been any interference by the government. The process has been very democratic," Jawed Ludin told reporters.