Brigadier Roger Lane told reporters he expected offensive operations, such as the British-led "Snipe" mission under way in the mountains of eastern Afghanistan, would end in a matter of weeks rather than months.
"We believe we're on the right way, that the fight against AQT (al Qaeda and Taliban) in Afghanistan is all but won, that they're not showing a predisposition to reorganize and regroup to mount offensive operations against us," Lane said.
The United States, supported by its Western allies and the interim government in Kabul, has spearheaded the pursuit of the austere Taliban movement, and remnants of Osama bin Laden's Qaeda network.
Bin Laden and his international network of Muslim militants hosted by the former Taliban rulers have been widely blamed for the Sept. 11 suicide attacks on the United States.
"I don't say it's (the war) over now, but I think it will be in the weeks to come rather than the months to come," Lane said.
Al Qaeda and Taliban fighters seem to have melted away since the last big battle of the Afghan war, when U.S. and Afghan government forces took on several hundred fighters in March.
Many Afghans believe both Taliban and Qaeda fighters have simply dispersed, lying low in rural areas and avoiding direct confrontation with the highly mobile and superior firepower of the Western forces.
While U.S.-led forces concentrate their search for fugitive Taliban and al Qaeda in eastern Afghanistan, the factional fighting that has plagued parts of this war-shattered nation hit southern Kandahar, the spiritual heartland of the deposed Taliban, police said Wednesday.
One person was wounded in an exchange of gunfire between unidentified groups in the southern administrative hub early Wednesday morning, they said.
It is unclear whether the injured person was participating in the shooting or caught in the crossfire, but officials noted that the incident might have stemmed from a shootout Monday night between a half dozen soldiers and several police officers in which one soldier was killed.
The outbreak in Kandahar appeared to be a smaller scale version of factional fighting that has beset other areas — near Mazar-e-Sharif in the north and Gardez and Khost in the southeast, where up to 28 people were killed, and more than 800 rockets fired into the city in just four hours.
The fighting usually centers around turf battles between warlords seeking to control areas in defiance of regional governors appointed by the national interim government.