Serbia has rejected a proposal from Montenegro that the two end their union and form independent nations.
Kostunica said he remained committed to the 2003 deal
Serbian Prime Minister Vojislav Kostunica said the plan was a serious breach of an agreement signed in Belgrade in 2003 under EU auspices.
This established a union of what remained of Yugoslavia after the bloody Balkan conflicts.
Under the agreement, neither side is supposed to propose complete separation before 2006.
Montenegro's president and prime minister proposed the disintegration of Serbia-Montenegro on Tuesday, suggesting that the two former Yugoslav republics recognise each other as sovereign states.
But in a letter to President Filip Vujanovic and Prime Minister Milo Djukanovic, Mr Kostunica said: "The proposal that you have sent to me represents a serious breach of the Belgrade accord.
"I remain committed to what we have signed."
Once part of a six-republic Yugoslav federation, Serbia and Montenegro retained links when four other republics seceded in the early 1990s.
Serbian officials have aimed to maintain the union, despite growing pro-separation feeling on both sides.
Serbia and Montenegro have substantial autonomy under the 2003 deal, sharing only a limited central administration in charge of foreign and defence affairs.