Gen. Haji Saifullah Khan, the main Afghan commander in the battle area in Zabul province's Dai Chupan district, said U.S. warplanes and helicopter gunships kept up their barrage until shortly before dawn Tuesday.
Khan said the Taliban had been pushed back from three hideouts Tuesday but were continuing to hunker down, using the rough terrain as their shield.
"It's a huge mountain with many gorges in it. It provides very excellent shelter against bombing," said Khan, who spoke to The Associated Press by satellite phone from the front lines.
The commander said his men would offer the Taliban in other hideouts a chance to surrender — then move in.
"We have tightened our siege. We are very close to the Taliban positions," he said. "We will try to make them surrender. If they do not surrender then fighting will start."
Khan said U.S. warplanes targeted the Sairo Gar mountain area. His ground troops found bedding and turbans but no weapons at the three locations — Kafir Shaila, Kabai and Ragh — that were overrun. There was no ground fighting as the Taliban simply retreated from their positions.
The U.S. military has been involved in the fighting since it began about eight days ago. Since Saturday, they have dubbed their role in the skirmishes as "Operation Mountain Viper."
The military said U.S. special operations forces and soldiers from the 10th Mountain Division, as well as close air support, have been involved. The military would not say how many U.S. soldiers were involved in the fighting, though Afghan officials have put the number at several hundred.
U.S. military spokesman Col. Rodney Davis said Tuesday that coalition forces clashed with groups of five to 10 fighters firing small arms and rocket-propelled grenades in Dai Chupan. They had cornered a group of insurgents in a cave and were attacking it Tuesday afternoon with small arms fire, artillery and air support, he said.
"As a result of the offensive several anti-coalition elements have fled the area making them more vulnerable to attack," Davis said in a statement from Bagram Air Base, the coalition headquarters in Afghanistan.
There were no reported coalition casualties in the latest fighting, Davis said. He had no details on Taliban casualties.
One American soldier died Friday when he fell during a night combat mission. Two other U.S. soldiers died in a 90-minute gunbattle Sunday in eastern Afghanistan, near the border with Pakistan. Four suspected Taliban were killed in that fighting.
Those deaths bring to 35 the number of U.S. troops killed in action in Afghanistan, in addition to 162 that have been wounded, according to the U.S. military.
Afghan presidential spokesman Jawid Luddin said that more than 500 troops of the fledgling Afghan national army had been deployed in Zabul. So far, most of the fighting on the government side has been done by provincial militia forces.
Dozens of suspected Taliban have been killed in the ongoing battle in Zabul province. U.S. military said at least 37 insurgents had been killed in direct combat or air strikes. Afghan officials have put the toll much higher.
The U.S. military said it had also called in warplanes and fired artillery on Monday after five rockets landed near a coalition base at Shkin, in eastern Paktika province, near where the two U.S. soldiers were killed in fighting on Sunday.
Meanwhile, in Kabul a spokeswoman for the International Assistance Force said Tuesday that the recent arrests of several suspected terrorists and criminals in Kabul were "preventive."
Early Monday, Afghan authorities supported by peacekeepers from a NATO-led force that patrols the capital raided an apartment and arrested an unspecified number of people suspected of "terrorist and criminal activities."
ISAF spokeswoman Maj. Sarah Wood described it as a "big operation" and a "preventive measure." "The arrests were to protect Kabul, by preventing any further attacks on its institutions or people," she told The Associated Press.
She would not say what evidence was uncovered to implicate the arrested men in terrorist activities. She said they were being held for questioning, but she wouldn't give any details.
Khalil Aminzada, deputy chief of police of Kabul, said Tuesday that two suspects were arrested in the capital on Monday by Afghan authorities acting with some foreigners. Aminzada was not sure if the foreigners were from ISAF or the United States.
He identified one suspect as Qalam, allegedly a former commander of rebel leader Gulbuddin Hekmatyar, but did not name the other and or elaborate on what they were suspected of plotting.
He said three guns were taken from the home. It wasn't clear whether Aminzada was referring to the same raid.
The U.S. Embassy had no comment.
Hekmatyar is a former prime minister who opposed the Taliban during their rule. However, after their collapse in late 2001, he allied himself with the Islamic hard-liners to oppose the U.S.-led coalition and President Hamid Karzai's government.
The 5,000-strong ISAF force, established in December 2001 in the wake of the U.S.-led war that toppled the Taliban, is charged with making the Afghan capital secure.
Security in Kabul is good compared with the rest of the country largely because of the peacekeeping force, yet some residents say the city is overrun by thieves and criminals, many of them affiliated with warlords who are part of the government.
In June, ISAF suffered its worst-ever casualties when a suicide bomber driving an explosives-laden taxi killed four German peacekeepers and wounded 29 others. The chief of ISAF last month warned that Kabul was still be vulnerable to further terror attacks.
Two government ministers have been shot and killed in broad daylight in Kabul since ISAF was deployed. No arrests have been made.