The Holy Synod of the Serbian Orthodox Church said: "Every sensible person has to realise that numerous internal problems and the isolation of our country on the international scene cannot be solved or overcome with this kind of leadership."
The church said that "new people, acceptable to the domestic public and the international community" should take over the administration.
"Faced with the tragic situation in our nation and our country ... we demand that the current President of the country and his government resign in the interest of the people and its salvation," the announcement continued.
The church has little spiritual impact on ordinary Serbs. But it has great political authority, especially among nationalists, who see it as the sacred custodian of the nation's history, values and relics.
Relations with Mr Milosevic have always been complicated. The church was generally associated with Serbia's expansionist wars in the Nineties, but its bishops turned against the regime after the 1995 Bosnian peace deal, which they saw as a sell-out. Many clergy blamed the outcome on Mr Milosevic's communist background.
The church is particularly associated with Kosovo; the seat of the Orthodox patriarch is in Pec, and the present Patriarch, Pavle, is a former bishop of the diocese of Prizren. The flight of Kosovo's remaining Serbs this week has undoubtedly appalled the hierarchy.
Mr Milosevic, an atheist, may shrug off the bishops' anathema. But the church will form a powerful ally for his former deputy prime minister, Vojislav Seselj, whose nationalist Radicals stormed out of the coalition government on Monday, denouncing the "betrayal" of Kosovo.Reuse content