BELGRADE (Reuters) -Kosovo must give greater autonomy to Serb-majority municipalities in the north of the country if it wants to move closer to joining NATO and the European Union, the U.S. envoy to the Western Balkans said on Wednesday.

Violence has flared since Kosovo authorities installed ethnic Albanian mayors in offices in the municipalities after they were elected in a vote in April on a turnout of just 3.5%, angering Serbs who form a majority in northern areas and who had boycotted the event.

Envoy Gabriel Escobar also urged Kosovo to withdraw police and mayors from their offices in Serb-majority areas to de-escalate tensions and then hold new municipal elections in which Serbs would participate.

Kosovo's President Vjosa Osmani in an interview on Wednesday told Reuters her country could trigger new elections in Serb-majority municipalities if 20% of voters sign a petition asking for them.

Escobar told reporters in the U.S. Embassy in Belgrade: "If Kosovo wants to move towards Euro-Atlantic integration it will have to establish (an association of Serb municipalities),"

"So it will happen. The question is, will it happen with this (Kosovo) government or a next, a future government."

Serbia, which backs around 50,000 Serbs in northern Kosovo both financially and politically, would have to ensure that the region's Serbs took part in the new election, Escobar added.

Four predominantly Serb municipalities in northern Kosovo see Belgrade as their capital and are defying the government in Pristina.

The Serbs in north Kosovo left the country's institutions last December. They want greater autonomy, under the provisions of a 2013 EU-sponsored agreement which envisaged the formation of an Association of Serb Municipalities.

Prime Minister Albin Kurti is reluctant to implement the accord because he fears that if granted more autonomy, the Serbs could hold a referendum to join Serbia instead of staying as part of Kosovo.

Reinforcements for NATO's peacekeeping force began to arrive in Kosovo this week following the recent unrest.

Kosovo declared internationally recognised independence from Serbia in 2008, nearly a decade after NATO bombing drove the Serbian army and police from the territory. Serbia still regards Kosovo as its southern province.

(Reporting by Ivana Sekularac; editing by Aleksandar Vasovic, Gareth Jones and Angus MacSwan)