Afghan forces are struggling to hold the police HQ in the town of Sangin in Helmand province, amid a siege by Taliban fighters, officials say.
But there are conflicting reports as to who controls the whole district.
The Helmand governor and police dismissed Taliban reports that it now controlled it as "totally false".
Sangin district has fallen to Taliban control several times and the fighting has caused significant casualties among Afghan and international forces.
In the east, a Taliban attack near Bagram on Monday killed six US soldiers. It was one of the deadliest attacks on foreign forces in Afghanistan this year.
Three rockets were also fired into Kabul overnight on Monday.
Some 12,000 foreign soldiers are deployed in the country as part of the Nato-led Resolute Support international coalition, which is meant to underpin Afghan security forces.
Britain has announced that a small number of UK personnel have been deployed to Camp Shorabak in Helmand province in an advisory role. The BBC understands there are 10 such personnel.
"These personnel are part of a larger Nato team, which is providing advice to the Afghan National Army. They are not deployed in a combat role and will not deploy outside the camp," a Ministry of Defence spokesman said.
Resolute Support replaced the 13-year Operation Enduring Freedom, which saw more than 900 international coalition deaths in Helmand province. More than 100 of them were British soldiers.
The head of Helmand's provincial council, Muhammad Kareem Atal, said 2,000 Afghan security forces personnel had been killed in the province this year.
'Supplies running low'
Police officers and soldiers inside the Sangin police headquarters appeared to be still holding out on Tuesday morning.
The district police commander, Mohammad Dawood, earlier 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.
Mr Dawood said that over the past month, security forces in the district had sustained 365 casualties, both dead and injured.
It is unclear whether the authorities or the Taliban are in control of Sangin.
Helmand Governor Merza Khan Rahimi said Afghan forces "are in Sangin district and there are some clashes, but the district is in our control".
An Afghan army officer however told the BBC there was still fighting going on in Sangin and that the Taliban now controlled most of the district.
"At the moment we are controlling the police headquarters, the Army National Army Battalion base and the district governor's headquarters," he said.
The Taliban said they controlled most of Sangin town and the main administrative building had been abandoned.
Why is Sangin important? Inayatulhaq Yasini, BBC Afghan
Sangin was once the centre of operations for international forces in Afghanistan.
Regaining full control of it 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.
Keeping control of the centre of Sangin will not be easy for the Taliban, but resentment of government troops is high following military operations which locals say wrought unwarranted destruction.
If the government wants to control the area, it should look to win hearts and minds - a strategy once trumpeted by the foreign forces here.
Separately, reports say the Taliban are also close to overrunning the neighbouring district of Gereshk.
Mr 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.