Kandahar is in chaos following the Taleban surrender
Speculation has intensified over the location of the pair after a cave complex believed to be Bin Laden's main base was seized and Mullah Omar's stronghold of Kandahar fell to the opposition on Friday.
Mr Karzai - who is to lead Afghanistan's interim government after the rout of the Taleban - said he was convinced that both men were still within Afghanistan, despite reports that they may have slipped into neighbouring Pakistan.
The military authorities in Pakistan have meanwhile deployed helicopter gunships and extra troops along its 2,500km (1,500 mile) border with Afghanistan, hoping to make the border impenetrable for anyone trying to escape.
Mr Karzai has dismissed suggestions that Mullah Omar might be offered an amnesty, insisting that that both men would be made to face international justice if they are caught.
There is a $25m bounty on Bin Laden's head.
In other developments:
The BBC's Katty Kay in Washington says the US would prefer both men to be caught and killed by opposition forces on the ground, eliminating the political risks of putting either on trial.
The US administration is still undecided as to what to do with the Taleban leader and his top commanders if they are captured alive, according to General Tommy Franks, chief of the US Central Command.
"Do we demand to take them ourselves out of Afghanistan or could they perhaps be handled in some other way by the government within Afghanistan?" he said.
"I'm not sure what policy decision will be taken on that issue."
Sealing the border
Across the border in Pakistan, hundreds of army troops have been deployed, not just at the regular checkpoint in the north-west frontier province of Baluchistan, but at dozens of key points along the border.
In addition, an army spokesman said helicopters armed with machine guns were patrolling the region, leaving little room for any illegal movement.
The deployment is said to be particularly intense in the region close to the Tora Bora caves in Afghanistan, where the US-led military operation is currently going on against the suspected al-Qaida members.
The hunt for Mullah Omar in Kandahar has been complicated by the rising tensions among rival factions of the opposition.
At least three tribal groups are vying for power in the city, with some said to be unhappy with their share of the spoils of the victory negotiated by Mr Karzai.
One is comprised of forces loyal to Mr Karzai. Gul Agha, the former governor of Kandahar, heads another, while a third is led by another opposition leader, Mullah Naqibullah.
The rival leaders are due to attend a shura, or city council, within the next few days to try to bring an end to the clashes and restore some form of civic administration.