Supporters of former president Burhanuddin Rabbani accused the government of trying to force them to accept a presidential system, which they say would put too much power in the hands of U.S.-backed Afghan leader Hamid Karzai.
Many in the assembly — called a loya jirga or "grand council" — are calling for the creation of a powerful prime minister's post to blunt some of the president's influence, something Karzai has come out strongly against.
Several delegates have threatened a walk-out over the issue, and others signed a petition Wednesday saying the issue of divvying up power should be decided before the council takes up other hot-button issues like women's rights and the role of Islam in a future state.
"A large group of delegates stood and shouted that they would walk out if the jirga continues in this manner (without a decision on the prime minister)," Mohammed Daoud, a delegate from Bamiyan, told The Associated Press. The session was closed to the media.
About 200 of the 500 loya jirga delegates signed a petition calling for a quick decision on whether to create a prime minister, said delegate Hafiz Mansour, a Rabbani supporter and editor of a Northern Alliance weekly newspaper.
But Karzai played down the controversy, saying a walkout was unlikely.
"I don't think they'll walk out of the jirga," he said on the steps of his palace office. "The jirga will go on and it depends on the delegates of the jirga what they decide."
He called Rabbani a "very sensible man" and added: "I don't think that he would let his people do something like that."
The council's morning session produced more fireworks, after a female delegate, Malalai Joya, denounced faction leaders such as Rabbani.
"Why have you again selected as committee chairmen those criminals who have brought these disasters for the Afghan people? In my opinion they should be taken to the world court," said Joya, a delegate from Farah province.
Many of the commanders who fought the Soviet Union in the 1980s still control provincial fiefdoms and have been accused of human rights abuses and corruption. After ousting the Soviets, the militias turned on each other in a brutal civil war that destroyed most of the capital, Kabul.
Some faction leaders, like former president Rabbani and Abdul Rasul Sayyaf, a deeply conservative Islamist, have been elected to the jirga, and others — like northern strongman Abdul Rashid Dostum — were appointed by Karzai.
Human rights groups and others have warned that Karzai will bargain away too much to the men in return for their support for a presidential system.
Joya's comments, which stopped only after her microphone was turned off, sparked outrage among the hardliners and their supporters, who denounced her as a communist and demanded she be removed from the session amid shouts of "God is Great!"
Council chairman Sibghatullah Mujaddedi, a Karzai ally, ordered Joya thrown out, saying she had "disturbed this jirga and been very rude."
As Joya resisted security guards that had come to accompany her out, Rabbani made a call for tolerance, and she was allowed to remain.
The flare-up was a sharp reminder of the fractured politics that still dominates Afghanistan after more than two decades of conflict.
The first three days of the jirga have been marked by endless squabbling over the method of voting for leadership positions, a parade of self-indulgent monologues and a one-day stall to allow about 60 delegates to attend the opening of the Kabul-Kandahar highway.
The jirga broke into 10 different groups Wednesday afternoon to debate different parts of the 160-article draft constitution. It was not clear how many days they would meet for before returning to the plenary session.
The committees will be debating such issues as the role of women in society, the place of Islam in a future state and the balance of power in a nation accustomed to fighting over it.
According to the New York Times, women at the conference were already miffed when the chairman opted not to name a woman as one of his deputies. He reversed the ruling later, but women were still riled by his remark that they should not make the mistake of considering themselves equal to men.
Delegates also predicted testy debate over which of Afghanistan's main languages — Dari or Pahsto — should be used for the national anthem, and whether higher education should be free.
The council is meeting under intense security amid warnings by the U.S. military that Taliban rebels might try to target the gathering. Early Tuesday, three rockets slammed into Kabul, but none landed near the site of the council.
That same night, one German peacekeeping soldier was shot by gunmen as he approached them on a darkened street, said peacekeeping spokesman. Lt. Col. Joerg Langer. His bulletproof vest stopped the bullets, and he was not injured. The gunmen escaped.