At least 12 Taliban fighters have been killed in the week-old offensive which US officials hope will snare al-Qaida leader Usama bin Ladin.
The three Taliban commanders were arrested on Friday in a raid on a house in Zabul province in a joint US-Afghan operation, said General Fatih Khan, an Afghan army officer based in the south-east of the country.
US-led forces were hunting a former Taliban provincial governor, Mullah Abd Al-Razzaq, when they caught the three, identified as Mullah Niamat Allah, Mullah Salih Muhammad and Mullah Balush. Many weapons were seized, he said.
It was not clear how senior the three captured men were and US authorities were not immediately available for comment.
The 12 Taliban fighters were killed in an air-strike on their truck in Kandahar province on Thursday, Afghan army officers said.
They were the first reported casualties in Operation Mountain Storm, which began on 7 March and involved troops from the 13,500-strong US-led force backed by air support.
Pakistan forces, helped by some tribal fighters, are sealing the Pakistan side of the mountainous Afghan border to stop Taliban supporters hiding in Pakistan's remote tribal lands.
US forces hope their military
clampdown will net bin Ladin
The fresh campaign comes after a surge in attacks on aid workers and foreigners, as well as against Afghan and US-led forces.
US defence officials have described Mountain Storm as a broad spring offensive to hunt down al-Qaida fugitives, including bin Ladin.
The push was timed to exploit improving weather in the region between Afghanistan and Pakistan, where bin Ladin is believed to be, they said.
Afghan soldier killed
An alliance of the Taliban, al-Qaida and forces loyal to ex-Afghan PM Qalb al-Din Hekmatyar are believed to be regrouping in the border areas.
On Saturday, Taliban armed with rockets and heavy machine guns attacked a government office near the Afghan-Pakistan border, sparking a firefight that killed one Afghan soldier and three Taliban fighters, police said on Sunday.
The attack occurred in the Shorovak district of Kandahar province, 180km south-east of the southern city of Kandahar, Kandahar deputy police chief General Salim Khan said.
The attack occurred in Shorovak
district of Kandahar province
About 60 Taliban fighters attacked the office of the Shorovak district chief, Khan said.
Tracks of the vehicles carrying the Taliban showed they came from across the border in Pakistan, and retreated there after the fight, Khan claimed.
The bodies of the three slain Taliban were being held on Sunday in the district office, he added.
Two Afghan soldiers wounded in the fight were said to be in good condition.
Also late on Saturday, two rockets hit the capital of Afghanistan's eastern Laghman province, killing one civilian.
A rocket tore through the roof of the man's home in Mehtarlam, Laghman's capital, Governor Muhammad Ibrahim Babkerkhel said on Sunday.
The second rocket landed in an open field near Babkerkhel's home, shattering windows there and at several nearby houses.
A man claiming to be a spokesman for the ousted Taliban, who identified himself as Qari Mahmud, said: "we carried out this attack".