His nominated replacement, Lt. Gen. Agim Ceku, heads the civil emergency organization that ethnic Albanians view as the core of their future army.
Ceku sided with Croatia's army in their fight against Serbs during the breakup of Yugoslavia in the early 1990s. Serbian officials have accused him of committing war crimes against civilians and have issued a warrant for his arrest. Ceku, 44, denies any wrongdoing.
He became the commander of the now-disbanded Kosovo Liberation Army, the guerrilla force that fought Serb troops during the province's 1998-1999 war.
U.N. Secretary-General Kofi Annan last month offered a grim assessment of Kosovo's progress toward stability, saying in a report that the region had fallen behind in efforts to create a multiethnic and democratic society.
Annan's report to the U.N. Security Council said there had been little headway in efforts to achieve a series of benchmarks including the rights of minorities, ending corruption and the return of refugees.
Serbian leaders in Belgrade want to keep at least some control over the province, which has been a de-facto U.N. protectorate since the end of the war.
Western officials are eager to see a solution by the end of 2006.
The U.N.'s chief envoy for the Kosovo talks, former Finnish President Martti Ahtisaari, said Wednesday that the province's remaining negotiators assured him "that the process of negotiations will continue with increased vigor."
"I have no doubt that that will be the case," he said.
Kosumi became prime minister after the resignation of his predecessor, Ramush Haradinaj, who was indicted last year for war crimes by the U.N. war crimes tribunal in The Hague, Netherlands.