Delegates taking part in the Loya Jirga, or grand assembly, are meeting in tents set up at the Kabul polytechnic campus to debate and ratify the draft constitution.
The draft constitution is expected to pave the way for the country's transition to democracy in elections scheduled for June 2004.
The convention was opened on Sunday by former King Muhammad Zahir Shah. But little debate has so far taken place on the constitution, with the first few days taken up with procedural matters.
The 502 delegates, including some 100 women, have been divided into 10 groups to discuss the controversial document and debate the country's future form of government.
Some have, however, called for a boycott of the convention unless the key issue of whether to have a presidential or parliamentary system is debated by the whole gathering rather than in separate groups.
Delegates are divided between those who support the strong presidential system laid down in the draft and those, including some anti-Soviet fighters' factions, who prefer some form of prime minister or a parliament to counterbalance sweeping presidential powers.
"They will have to work very hard to reach a consensus"
Manoel de Almeida e Silva,
President Hamid Karzai has repeatedly said he will only stand in
next year's presidential polls if the loya jirga approves the system laid down in the draft document.
Several delegates have backed Karzai's view that a strong presidential system was needed as the country lacked mature
political parties for a successful parliamentary democracy.
"They will have to work very hard to reach consensus," said UN spokesman Manoel de Almeida e Silva.
While presidential system versus parliamentary has been the main sticking point so far, women delegates are also calling for equal rights to be enshrined in the constitution.
Article 22 says the "citizens of Afghanistan have equal rights and duties before the law" but does not explicitly state that women have equal rights.
Under the rule of the ousted Taliban, women and girls were denied education and effectively barred from public life.
"We want the explicit mention of 'women and men' in every article where the words 'Afghan citizens' are used"
southeast Ghazni province
"We want the explicit mention of 'women and men' in every article where the words Afghan citizens are used," said Noorya Wisal from southeast Ghazni province.
The United States has also raised concerns about the extent to which religious freedom is protected due to the wording of the draft.
"Freedom of religion is neither denied, but it's certainly not fully guaranteed," said the US ambassador-at-large for international religious freedom, John Hanford.
Streets around the loya jirga site have been sealed off while foreign peacekeepers, newly-trained Afghan soldiers, police and secret service agents provided tight security. They face threats from Taliban fighters, who claimed responsibility for three rockets which hit Kabul early on Tuesday but hurt no-one.