The decision, taken Thursday after scores of delegates refused to take part in a vote on several amendments to the draft charter, was the latest setback for the historic gathering, which has already been marred by acrimony and a dangerous ethnic rift.
Opponents are particularly angry over Karzai's insistence on the creation of a strong presidency, which they say could shut minorities out of the halls of power.
Officials said more than half of the 502 members of the loya jirga cast their ballots in voting Thursday — enough to make the results binding. But after hours of behind-the-scenes wrangling, the meeting was called off until Saturday to allow more time to seek a compromise.
Karzai insists a simple majority of those voting is enough to pass the charter, but most observers recognize that a constitution that doesn't win wide-ranging support will hamstring the country as it seeks to put two decades of devastating conflict behind it.
Meanwhile, U.S. troops and helicopters killed as many as 14 insurgents in clashes in the mountains of eastern Afghanistan, the military said Thursday.
Three U.S. soldiers were wounded in the battle Wednesday some 20 kilometers (12 miles) northeast of Shkin, a town in Paktika province near the Pakistan border.
The first three militants were killed in a gunbattle after a small group of insurgents fired on a U.S. patrol, spokesman Lt. Col. Bryan Hilferty said.
The same patrol later found the insurgents, and AH-1 Cobra attack helicopters flying in support inflicted several more casualties, Hilferty said.
"We don't know for sure, but we think 11," he said. "It was getting night and we didn't go to see the bodies."
One of the wounded American soldiers was evacuated and is in a stable condition, Hilferty said. The other two immediately returned to duty.
Suspected Taliban and al-Qaeda militants regularly attack U.S. and allied Afghan forces as well as government and aid workers in a broad swath of southern and eastern Afghanistan along the rugged Pakistani frontier.
The U.S. military, which still has more than 11,000 troops here, says it killed 10 militants and detained more than 100 people in a four-week operation in the border regions called Avalanche which ended Monday.
Afghan, U.S. and U.N. officials have urged Pakistan to prevent insurgents from using the country as a base for cross-border attacks.
Pakistan, a key ally in the United States' war on terrorism, insists it is doing all it can.