US aircraft have carried out two attacks in Sangin, the district in southern Afghanistan overrun by Taliban fighters this week.
The official statement came as the battle for the strategic Afghan province of Helmand continued.
"US forces conducted two strikes in Sangin on December 23 against threats to the force," a spokesman for the military coalition said on Thursday.
Earlier in the day, Afghanistan's government sent reinforcements to help besieged forces as the Taliban claim to have taken control of almost all of Sangin.
The Taliban spokesperson, Zabiullah Mujahid, said on Wednesday that their fighters had seized the entire district including police and military installations and their flags had been raised.
However, Helmand's deputy governor, Mohammad Jan Rasoolyar, denied the claim.
"We are still fighting to push back the Taliban. Parts of Sangin are under the Taliban control but not the police and military installations," he told Al Jazeera.
"The military planes have dropped food and supplies to the Afghan forces on ground."
Read more: Fierce fight for Helmand as Afghan Taliban gains ground
The UK Ministry of Defence said on Tuesday that British troops had been deployed to the province to support local forces after the Afghan Defence Minister called for a desperate international support and air cover.
"As part of the UK’s ongoing contribution to NATO’s Resolute Support Mission, a small number of UK personnel have been deployed to Camp Shorabak in Helmand Province in an advisory role," a spokesman said.
"In total the UK has around 450 troops in Afghanistan mentoring and supporting the Afghan National Defence and Security Forces and the Afghan Security Ministries."
Sangin has seen more than 100 British troops losing their lives during the decade long combat mission in Afghanistan.
The Taliban statement regarding the British troops deployment said that before entering Afghanistan "they should have studied the history of their ancestors and should have learned a lesson from the repeated defeat".
"For that reason they would have not come with the intend to invade our country," the statement said.
"They were defeated even after the presence of thousands of troops and the same will happen with these few hundred troops, this means nothing else but a shameful humiliation for them.
"They have made no accomplishment even after fighting for the past 14 years. We are still strong."
Read more: Residents stranded as battle for Helmand intensifies
David Sedney, a foreign policy analyst at the Wilson Center in Washington DC, told Al Jazeera that the Afghan army is showing its weakness.
"The Taliban have made big advances in Helmand province in summer and into the winter and the offensive is increasing," he said.
"They [Taliban] put a lot of fighters a lot of weapons in Helmand province that is right in the border with Pakistan and most of the fighters and weapons come across the border, there is nothing that stops them.
"The Afghan National Army core that was charged with the defending Helmand was the newest one and when the United States and NATO pulled back, they decided not the leave any serious advisors with them, just a few special forces troops, so you have force that is poorly equipped and is really struggling to survive."
No end to violence
The northern city of Kunduz briefly fell to the Taliban in late September - the biggest victory for the group in 14 years of war.
Earlier this week, a suicide bomber attacked a joint Afghan-NATO convoy near Bagram airbase near Kabul, killing six foreign soldiers and wounding three others.
The Taliban claimed responsibility.
"Of late, the Taliban has shown an extraordinary capability to launch major attacks on government forces. They have proven capable of using both guerrilla fighters and engaging in conventional warfare," Hashmatullah Moslih, Al Jazeera political analyst, said.
"At the same time, the government soldiers are static - sitting in their outposts defensively, effectively handing the initiative to the Taliban."
This month marks a year since the US-led NATO mission in Afghanistan transitioned into an Afghan-led operation, with allied nations assisting in training local forces.
US President Barack Obama announced in October that thousands of US troops would remain in Afghanistan past 2016, keeping the current force of 9,800 troops, amid a surge in Taliban attacks.
Additional reporting by Shereena Qazi. Follow her on Twitter @ShereenaQazi
Source: Al Jazeera And AFP