“Serbs have to remain and survive in their homes in Kosovo,” Mr. Vucic told the skeptical audience of ethnic Serbs in the village of Banjska in northern Kosovo. “We cannot allow our numbers to dwindle in the land we’ve lived in since ancient time.”

Still, he made clear that it was imperative that both sides act in good faith in the wake of Mr. Ivanovic’s killing in the northern city of Mitrovica, not far from the monastery. The investigation is an opportunity for the ethnic Albanian institutions to “show what they will do,” he said in a statement. On the Serb side, he said, “There will be no mercy for the perpetrators nor for those who ordered it, no matter whether their name is Serbian or Albanian.”

The war ended nearly two decades ago, but tensions remain high and all sides are aware how quickly violent episodes in one ethnic community can morph into a conflict with another. Mr. Vucic’s arrival was precipitated by the death of Mr. Ivanovic, 64, who was shot five times in the chest on a street, his body splayed out on the sidewalk just steps from the office of the political party he led.

As Mr. Vucic’s motorcade sped from the north to a Serbian enclave in the south of the country, hundreds of officers lined the highway, standing guard in a blinding snowstorm.

The Serb leader tried to walk a fine line on his visit, working to satisfy different audiences — the Serbian people, and the Western leaders he is courting as he seeks to join the European Union.