Nato General Secretary Jens Stoltenberg said “all necessary actions” would be taken for a “safe and secure environment”.
On Sunday, Kosovo’s prime minister Albin Kurti accused Serbia of carrying out a “terrorist attack” on its territory after a policeman was killed, apparently by a heavily armed gang of up to 30 men who then took shelter in a monastery.
The stand-off, in the Kosovan village of Banjska, close to the border with Serbia, underlined simmering tensions in the Balkan region.
By evening the men were said to have barricaded themselves into the monastery and had also suffered casualties. Kosovo said that three of the gunmen had been killed in shootouts during the day.
“Organised crime, which is politically, financially and logistically supported by Belgrade, is attacking our state,” Mr Kurti said.
“It is clear that these uniformed people are an organised professional unit who have come to fight in Kosovo. There are at least 30 professional, military or police armed people who are surrounded by our police forces and whom I invite to surrender to our security agencies.”
The incident started after a Kosovan police officer was killed in an attack by the gang at 3am on Sunday. Another officer was injured. Police had been called after reports of a blockade in Banjska. Three police units came under fire but pushed back the attackers, who then fled to the monastery.
US officials are monitoring a large deployment of troops along the border with Kosovo.
British troops will help form part of the KFOR peacekeeping force, which comprises of around 4,500 troops from about 27 Nato and partner countries.