The drama in Yugoslavia is being played out against intense international pressure for Mr Milosevic to step down, with many Western leaders warning the Yugoslav leader against any attempt to steal victory and offering to lift crippling sanctions against Yugoslavia if he was replaced.
In one of the strongest Western reactions, the British Prime, Minister Mr Tony Blair, declared at the Labour Party conference in Brighton: "I say to Milosevic. You lost. Go. Your country and the world has suffered enough."
The French Foreign Minister, Mr Hubert Vedrine said in a statement in Paris: "Whatever the authorities in Belgrade may say, it seems now undeniable that Slobodan Milosevic has lost and that Vojislav Kostunica has won."
Russia, meanwhile, appealed for calm in Yugoslavia after Sunday's presidential vote and said the elections could be viewed as fair.
"The first round of the presidential election has already demonstrated the considerable democratic potential in Yugoslav society. Now it is vital to preserve civil peace and stability in the country," the Foreign Ministry said in a statement.
"It is also important that all political forces refrain from any kind of confrontation," it said.