Prime Minister Albin Kurti has urged the gunmen in the village of Banjska near the Serbian border to surrender.

He blamed "Serbia-sponsored criminals". Serbia has not commented.

The Nato-led peacekeeping force in Kosovo says it has troops in the area and is ready to respond if required.

Sunday's shooting began at about 03:00 (01:00 GMT), after police said they arrived in Banjska where a blockade had been reported.

Officers were attacked from several different positions with "an arsenal of firearms, including hand grenades and shoulder-fired missiles", they said in a statement.

"We can see armed people in uniforms... they are firing on us and we are firing back," Kosovo police official Veton Elshan told AFP.

Mr Kurti said they were "professionals, with military and police background".

The Serbia Orthodox Church said that gunmen had stormed a monastery in the village, located in Leposavic, where pilgrims from the northern Serbian city of Novi Sad were staying. 

Priests and pilgrims locked themselves inside the monastery's temple for safety, the Diocese of Raska-Prizren said.

"Armed masked men move around the courtyard and occasional gunshots are heard," it said in a statement condemning the violence.

Tensions have run high in Kosovo, after violent clashes followed a disputed local election in May and EU-mediated political talks designed to stabilise the situation have stalled.

Kosovo declared independence in 2008 but Serbia - along with Belgrade's key allies China and Russia - does not recognise it.

Many Serbs consider it the birthplace of their nation. But of the 1.8 million people living in Kosovo, 92% are ethnic Albanians and only 6% are ethnic Serbs.

The EU's foreign policy chief Josep Borrell condemned what he called the "hideous attack" and said those responsible must be brought to justice. 

But Kosovo's foreign minister, Donika Gervalla-Schwarz, criticised Mr Borrell's statement, saying it did not express support for the police nor use the word "terrorists" to describe the attackers.