The prospect of imminent Nato raids against Serbia is looming large. "Nato is ready to take whatever measures are necessary ... these include air-strikes," the secretary-general of the alliance, Javier Solana, said.
Mr Hill went to Belgrade for a last-ditch effort to persuade the Yugoslav president to allow Nato peace-keepers into the Serbian province and thus remove the main obstacle to a settlement at the Rambouillet talks by thedeadline of 11am GMT.
If Mr Milosevic does not relent, strikes against military targets could be launched in days, conceivably hours - a message conveyed in a personal telephone call by the US Secretary of State, Madeleine Albright, on Thursday. But Mr Milosevic showed no sign of blinking, telling a Cypriot delegation that Belgrade would not give up Kosovo "even if we are bombed".
President Bill Clinton said yesterday that he saw no option but to use force against Yugoslavia if it fails to embrace a peace agreement on Kosovo, and he rejected extending today's deadline to reach an accord. "We ... stand united in our determination to use force if Serbia fails to meet its previous commitment to withdraw forces from Kosovo, and if it fails to accept the peace agreement," Mr Clinton said at a news conference in Washington with the French President, Jacques Chirac.
Mr Chirac urged Mr Milosevic to "choose the path of wisdom and not the path of war".
While Nato has drawn up plans for raids, planners recognise that conflict with Belgrade would be fraught with danger. Some 430 warplanes, including 260 US aircraft - among them F-117 Stealth bombers, B-52s and B-2 bombers, are massed, on 48-hour standby, to attack in Nato's Operation Noble Anvil.
Mr Milosevic has tried to exploit divisions within the Contact Group of countries in the negotiations, and Russia, his traditional friend in the six-nation body, has been voicing ever louder its opposition not only to air strikes, but also to the presence of Nato peace-keepers.
As Mr Milosevic spoke, thebrinkmanship intensified, with foreign missions in Belgrade withdrawing non-essential staff. Several governments, including Britain, the US and Germany, advised their nationals not to go to Yugoslavia, and to leave if they were already there.
At the same time, dignitaries - including Robin Cook, the Foreign Secretary, co-chairman of the conference, which started on 6 February - were arriving in Rambouillet for its end. But an admission of failure seemed in store rather than the announcement of a deal granting Kosovo wide autonomy and ending a year-long war that has killed 2,000 and driven 300,000 people from their homes.
"It looks very tough to reach a settlement, but we will be making every effort right down to the wire," Mr Cook said as he left for Paris, where he was to meet his French counterpart and co-chairman, Hubert Vedrine, and possibly Mrs Albright.
Closing one possible avenue of compromise, the Russian mediator, the Deputy Foreign Minister, Boris Mayorsky, denied that Russia was trying to win over Mr Milosevic by offering to deploy its own troops in the planned 28,000-strong force.
Complicating matters further, some negotiators for the ethnic Albanians, who constitute 90 per cent of the population of Kosovo, were criticising a deal they had earlier seemed to accept. Angry at the absence of any reference in the 60-page final draft agreement to a referendum that would lead to independence, they accused the Western mediators of excessively favouring Belgrade.
If the Albanians balk at the deal, punishing Mr Milosevic alone would be much harder for Nato to justify.