The Serbian leader has begun recruiting an armed police force which Montenegrin leaders fear he will use as a fifth column inside their country, the only Yugoslav republic that has not left the Serb-dominated federation. The result could unleash a bloody civil war as a diversion from Mr Milosevic's own domestic troubles.
Yesterday, Montenegro's Foreign Minister, Branko Perovic, described the Serbs' move as "illegal" and "unconstitutional".
"It's a provocation," he told The Independent on Sunday. "It's their way of seeking to provoke the situation." The pro-Milosevic force would be backed up by the still-powerful Yugoslav army in Montenegro, if there is a clash of wills between the two sides.
Montenegrin officials warn that such clashes could make even previous Balkan horrors pale. Miodrag Vukovic, chief strategist of President Milo Djukanovic, warned: "I'm afraid Milosevic will make conflict in Montenegro." If that happened, he said, "You can forget Bosnia, Kosovo, everything. It would be like brother fighting brother."
Montenegro has been increasingly trying in recent months to escape the dead hand of Belgrade. A referendum on independence, unthinkable until recently, is due to take place before the end of the year. Montenegrins will be asked to decide whether they want a looser form of federation with Serbia. But although talks are due in Belgrade this week, Mr Milosevic has shown no sign of acceding to such a proposal.
Vojislav Seselj, a powerful Serb nationalist leader, confirmed from Belgrade that the Montenegrins' fears of conflict if they tried to go it alone were justified. He said: "[Secession] can't happen without war, because the Montenegrins are Serbs."
The Montenegrins are unwilling to back down, however. Mr Perovic insisted: "This is our last offer - this is our minimum. We won't accept any answer but `yes'. No `yes, but...'."
The Montenegrin parliament looks set to raise the stakes this week by voting for a separate Montenegrin citizenship - in effect, a warm-up act for independence.
In Serbia, there have been demonstrations against Mr Milosevic in recent days, and more seem likely. Yesterday Patriarch Pavle, leader of the Serbian Orthodox Church, said the opposition included good people who could run the country better - if only they ended their in-fighting. He also repeated his call for Mr Milosevic to be held to account for massacres of ethnic Albanians in Kosovo. Nato forces are currently investigating a site near Pec which may contain as many as 350 bodies. That would make it the largest mass grave discovered so far.
Serbs' reasons for protesting against the Yugoslav leader are varied and confused: demonstrators blame him for fighting the Kosovo war, for losing the war, or simply for the catastrophic state of the economy. Few Serbs have jobs, and many of those who do rarely get paid. Mr Milosevic's situation is precarious, but he is used to that, and he knows how to fight back.
Yesterday, according to the independent Beta news agency, police in northern Serbia prevented activists from the Alliance for Change, an anti-government group, from collecting signatures for a petition calling on Mr Milosevic to resign. The alliance's workers in Sombor, 105 miles north-west of Belgrade, where the municipality is one of several which has demanded that the president should go, were told petition-signing could take place only inside the organisation's offices.
Although police have detained activists in several cities, they have not stopped rallies from taking place.