Reports from the southern Afghan province of Helmand suggest Taliban militants are close to overrunning the strategically important town of Sangin.
Helmand's governor, Mirza Khan Rahimi, insisted the authorities were still in control but his own deputy said that Sangin had been overrun.
The Taliban said they controlled most of the town and the main administrative building had been abandoned.
In the east, a Taliban attack near Bagram killed six US soldiers.
It was one of the deadliest attacks on foreign forces in Afghanistan this year.
Some 12,000 foreign soldiers are deployed as part of the Nato-led Resolute Support international coalition, which is meant to underpin Afghanistan's own security forces.
The battle for Sangin comes a little over a year after the end of UK combat operations in Afghanistan, in which at least 450 soldiers were killed.
During its deployment in Helmand, the British military suffered its heaviest losses in Sangin.
Battle for SanginGovernor Rahimi gave a news conference in Helmand's provincial capital, Lashkar Gah, after his deputy, Mohammad Jan Rasulyar, said Sangin had been overrun by the Taliban late on Sunday.
Fierce gun battles were going on between the Taliban and the Afghan security forces, Mr Rahimi was quoted as saying on Afghan TV, and the government had sent back-up forces.
But Mr Rasulyar had told AFP news agency: "The Taliban have captured the police headquarters, the governor's office as well as the intelligence agency building in Sangin."
Quoted separately by the Associated Press, Mr Rasulyar said casualties among Afghan security forces were high, without giving figures. Only some army facilities had not been taken, he added.
Why is Sangin important? Inayatulhaq Yasini, BBC Afghan Service
Sangin was once the centre of operations for international forces in Afghanistan, a key district that linked Lashkar Gah, the capital of Helmand province, to the province's northern districts.
Regaining full control of Sangin would increase the Taliban's mobility in parts of northern Helmand and cut a key supply line for Afghan forces with Lashkar Gah. Sangin is also a rich opium production centre - meaning potential tax revenue for the Taliban from the drugs trade.
The big question now is whether the Taliban can maintain their recent territorial gains in the district. Keeping control of the centre of Sangin will not be easy, but resentment of government troops is high in the district following military operations earlier this year which locals say wrought unwarranted destruction to property.
If the government wants to wrest total control of the area from the militants, they should look to win hearts and minds - a strategy once trumpeted by the foreign forces which controlled this part of the country.
Read more on why Sangin matters
Police officers and soldiers inside the Sangin police headquarters had appeared to be still holding out as of Monday morning.
The district police commander, Mohammad Dawood, told the BBC the Taliban had completely cut the facility off from the rest of the province, and food and weapons supplies were running low.
"For the past two days we have been surrounded inside the police headquarters," he said.
"No one can move out because the checkpoints along the roads are gone. The roads between the district and Lashkar Gah and other districts are closed. We also have a number of injured troops and bodies here. In the last two days the fighting has been very heavy."
Mr Dawood added that, over the past month, security forces in the district had sustained 365 casualties, both dead and injured.
Meanwhile, reports say the Taliban are also close to overrunning the neighbouring district of Gereshk.
The head of Helmand's provincial council, Muhammad Kareem Atal, was quoted by AP as saying that "around 65%" of Helmand was now under Taliban control.
In September, the Taliban briefly overran the northern city of Kunduz in one of their biggest victories in 14 years of war.
Motorcycle bomberThe attack at Bagram, the biggest US military facility in Afghanistan, happened at around 13:30 local time (09:00 GMT).
A bomber mounted on a motorcycle reportedly attacked a patrol in a village near Bagram.
US officials identified the six dead soldiers as Americans, and said another two had been wounded along with one Afghan.
The Taliban said it had carried out the attack in statements to media.
In the Afghan capital Kabul, a US woman was killed at a gym, with her suspected attacker, a mullah, arrested. The woman was named as Lisa Akbari.
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