Mr Rumsfeld's comments came as the Pakistan-based Afghan Islamic Press reported that the Taleban's supreme commander, Mullah Muhammed Omar, had agreed to leave the militia's southern stronghold of Kandahar and turn the city over to two local Pashtun leaders.
However, the Pentagon says that although the Taleban has now lost control of two-thirds of Afghanistan, it does not believe the report.
Click here for map of the battlegrounds
Bombing of targets in Afghanistan by US warplanes continued on Friday, despite the start of the Muslim holy month of Ramadan.
During heavy air raids on Kandahar, US jets hit the Taleban foreign ministry building and a mosque.
Eleven civilians were reported to have been killed in the raids, but there has been no independent confirmation of this.
And US Central Command said a mosque in the town of Khowst, eastern Afghanistan, had been hit by a 500-pound bomb, aimed at an al-Qaeda facility, which had gone astray.
In other developments:
- The UN special envoy for Afghanistan criticises the anti-Taleban Northern Alliance for delays in arranging a crucial meeting on the country's political future
- Pakistan begins deploying extra troops along part of its border with Afghanistan to prevent armed Taleban fighters from crossing into the country
- Militias in the eastern Afghan city of Jalabad struggle to agree on how to share power in the area after the Taleban pull out
- Between 2,000 and 3,000 Taleban fighters - thought to be mainly Arabs and Pakistanis - remain encircled in the northern city of Kunduz by Northern Alliance forces
- Russia is sending a delegation to Afghanistan to make contact with what Defence Minister Sergei Ivanov called "the leadership of the legitimate government" - a clear reference to the Northern Alliance
- Aid agency Oxfam has calls for immediate airlifts of food to Afghanistan where continued insecurity is making delivery of supplies increasingly difficult
Mr Rumsfeld said the US special forces in Afghanistan had sometimes met resistance and had to call in air support. Some had been wounded, but none had been killed.
"They're killing Taleban that won't surrender and al-Qaeda that are trying to move from one place to another," he told reporters.