Mr Holbrooke will tell the Yugoslav President bluntly that now Kosovo's Albanians have agreed in principle to a deal, Nato aircraft will start bombing Yugoslav military targets if he blocks the agreement.
The US emissary, architect of the 1995 peace deal that ended the savage ethnic war in Bosnia, arrived at noon. He was not expected to meet Mr Milosevic until today.
His task will be to cajole or bully the Serb leader into accepting the presence of a foreign military force in Kosovo to implement the three-year interim agreement.
Another US Balkan envoy, Christopher Hill, who met commanders of the rebel Kosovo Liberation Army on Monday, also travelled to Belgrade yesterday to increase the pressure on Mr Milosevic.
Western diplomats say the guerrilla leaders are ready to authorise a signing of the deal but remain opposed to the inclusion of Russian troops in any peace-keeping force.
The presence of fellow Orthodox Slavs is seen as a concession to Mr Milosevic, who might then be able to sell to his public the idea of a foreign army on Yugoslav soil.
Despite the now familiar display of brinkmanship, observers in Belgrade expect Mr Milosevic to agree to the deal, which is supposed to be signed by 15 March, when both sides are to gather in Paris for another round of talks.
"Now that the KLA has accepted the Kosovo peace plan, Milosevic will probably have to accept some kind of compromise," the authoritative VIP newsletter said yesterday.
"Milosevic most probably believes Holbrooke is his best chance for a good bargain."
Until now, the Yugoslav position has been that Belgrade might accept a political deal granting Kosovo autonomy for three years. But the stationing of foreign troops on Serbian territory would not be countenanced, certainly not a Nato-led force.
Mr Milosevic already knows his only chance to lift international sanctions will come if he strikes a deal on a Kosovo peace force.
Yugoslav officials are still talking tough. "We won't give an inch of our Serbian and Yugoslav territory," said a senior Socialist Party official yesterday. But this sort of hardline approach is intended only for domestic consumption.
In fact, the state-controlled media seems to be softening up the population for the eventual loss of Kosovo, and is not whipping up a frenzy of anti- foreign feeling. That is what happened the last time the Western alliance threatened the Serbs with heavy Nato air strikes. One Serb journalist based in Belgrade said: "At the end, it will be a relief not to have Kosovo."
In London, Nato's Secretary-General, Javier Solana, said Nato remained ready to launch air strikes if Mr Milosevic did not accept an autonomy plan for Kosovo. But he stressed that no Nato nation supported sending ground troops to fight their way into the province.
In Kosovo yesterday two Serb policemen were killed and three wounded when their vehicle hit a mine.
Yugoslav border authorities confiscated 90,000 German marks (pounds 35,000) from Bosnian Muslim pilgrims at the Yugoslav frontier with Bulgaria as they passed through on their way to Mecca.