The Assembly, or Loya Jirga, finally got underway in a giant tent erected at a polytechnic campus in the west of Kabul on Sunday.
The meeting is expected to last from 10 days to several weeks.
Vigorous debate is expected on many of the 160 articles of a published draft constitution.
But the central theme is expected to be the sweeping powers sought by US-backed interim President Hamid Karzai - powers which critics want diluted by a stronger parliament.
Uzbeks, Pashtuns, Tajiks and Hazaris have converged on Kabul from all corners of their diverse and troubled land for the meeting.
The outcome of the meeting and Afghanistan's progress towards elections is seen as a key test for rebuilding on America's other, even more troubled front, Iraq.
Signs have been mixed and Karzai has faced sharp criticism for seeking powers, some say verge on the dictatorial.
But Karzai, installed after the Taliban was overthrown at the end of 2001, has said he will only stand in elections next year if delegates agree to a strong presidency.
Karzai previously ruled out
running in presidential elections
On Saturday, he expressed confidence about an agreement, but predicted a tough debate.
Comments on constitution
The draft constitution and the Loya Jirga elections have been sharply criticised by foreign observers.
The International Crisis Group said the draft, backed by the United States, was unlikely to ensure democracy or human rights and risked failure like nine others before it.
Human Rights Watch said vote-buying and intimidation had ensured the assembly was stacked with proxies of regional commanders seen as the biggest obstacles to security vital for aid and reconstruction.
However, some delegates interviewed on Saturday agreed a strong presidency was needed, such as Muhammad Alam, a British-trained agronomist from Farah province.
"A country like ours emerging from civil war is not ready for a parliamentary system," he said, and analysts said Karzai appeared to be winning over the simple majority he needed.
But analysts say regional commanders, who control personal armies, and strongmen have been seeking pledges on greater autonomy, individual positions, or a stronger role for Islamic law in return for their backing - which could sow the seeds for future difficulties.