Karzai has faced fierce debate over his presidential plans
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Afghan President Hamid Karzai says the tribal council meeting in Kabul is expected to complete proceedings next week by adopting a new constitution.
Mr Karzai was confident the 500 delegates to the loya jirga would agree to his preference for a presidential form of government.
There has been fierce debate in the assembly between a presidential or parliamentary model.
After the constitution is adopted, June general elections should follow.
The BBC's Zaffar Abbas in Kabul says Mr Karzai's confidence suggests that those advocating a parliamentary system, particularly the Jamiat-e-Islami leader Burhanuddin Rabbani, have been marginalised.
Mr Karzai wants a presidential system with an elected parliament working under the head of the state.
He said the 10 committees that were given the task to go through the draft constitution had completed their work and was hopeful that by early next week Afghanistan would have its new constitution.
Ongoing battle
Mr Karzai's argument seems to have won over many delegates who fear a parliamentary system would be dominated by warlords.
Many delegates want to curb the powers of the warlords
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"If we wanted a coalition government we wouldn't have suggested a presidential government," Mr Karzai said.
"We have suggested the presidential system to avoid Afghanistan going towards conflict again."
The president still faces a battle with opponents who fear his powers will be too sweeping.
Some delegates, particularly the mujahideen, want a parliament with teeth to counter these powers.
But it is the standing of these former anti-Soviet fighters that other delegates want to curb.
One said: "If there is a presidential system they will become weak, their weapons will be collected and without their weapons and power these people are nothing."
The loya jirga, which is meeting in a massive tent in the capital, began 11 days ago.