In Leposavic, close to the border with Serbia, US peacekeeping troops in riot gear placed barbed wire around the town hall to protect it from hundreds of angry Serbs.
Later in the day, protesters threw eggs at a parked car belonging to the new Leposavic mayor.
Mr Vucic, who is the commander-in-chief of the Serbian armed forces, raised the army's combat readiness to the highest level, Defence Minister Milos Vucevic told reporters.
“This implies that immediately before 2pm (8pm Singapore time), the Serbian Armed Forces' chief of the general staff issued additional instructions for the deployment of the army's units in specific, designated positions,” Mr Vucevic said, without elaborating.
Nato peacekeepers also blocked off the town hall in Zubin Potok to protect it from angry local Serbs, witnesses said.
Mr Igor Simic, deputy head of the Serb List, the biggest Belgrade-backed Kosovo Serb party, accused Mr Kurti of fuelling tensions in the north.
“We are interested in peace. Albanians who live here are interested in peace, and only he (Kurti) wants to make chaos,” Mr Simic told reporters in Zvecan.
Serbs, who comprise a majority in Kosovo's north, have never accepted its 2008 declaration of independence from Serbia and still see Belgrade as their capital more than two decades after the Kosovo Albanian uprising against repressive Serbian rule.
Ethnic Albanians make up more than 90 per cent of the population in Kosovo as a whole, but northern Serbs have long demanded the implementation of a European Union-brokered 2013 deal for the creation of an association of autonomous municipalities in their area.
Serbs refused to take part in local elections in April, and ethnic Albanian candidates won the mayoralties in four Serb-majority municipalities – including North Mitrovica, where no incidents were reported on Monday – with a 3.5 per cent turnout.
Serbs demand that the Kosovo government remove ethnic Albanian mayors from town halls and allow local administrations financed by Belgrade to resume their work.
Last Friday, three out of the four ethnic Albanian mayors were escorted into their offices by police, who were pelted with rocks and responded with tear gas and water cannon to disperse the protesters.