Nine hours later that pledge was broken. Russian paratroopers, 200-strong, who had left their peacekeeping duties in Bosnia, were now in armoured cars and trucks pulling into Pristina, applauded by crowds of Serbs.
Nato and the Pentagon had been caught off-guard. The alliance had been told the troops would stop before entering Kosovo. They hadn't. The Russian foreign minister, Igor Ivanov, assured everyone it was a "regrettable mistake", and the troops would be ordered out.
But had it been a mistake? And who had given the orders and why? The evidence suggests that Moscow's audacious attempt to win the race into Kosovo - provoking a new crisis in its relations with Nato - came from top generals in the Russian ministry of defence. Resentful of the peace deal, and fearing the lack of an independent role in Kosovo, they ignored their own diplomats and deceived a US-led delegation in Moscow discussing Russia's place in the peacekeeping force.
The most plausible explanation - floated by well-placed sources in Moscow yesterday - is that Boris Yeltsin, the Russian president, or even a Kremlin official, issued vague orders that Russia's troops should enter Kosovo at the same time as Nato. The presidential staff and military knew that if that they did not move quickly, Nato forces would take complete control and "carve up" the province.
Russia would then have far less chance of winning its case, no matter how long it haggled with Strobe Talbott, the US deputy secretary of state, and his Pentagon aides; Nato would be in total command, and there would be no Serb-populated Russian sector in north Kosovo.
So the generals played their joker. Bypassing the Russian foreign ministry, they sent in the paratroopers, with instructions to take control of the Slatina airbase near Pristina.
It was a propaganda coup, a brazen nose-snubbing at the west that will be celebrated in the upper echelons of the military for months. "We have taken a little shine off Nato's so-called victory," one Russian colonel told the Independent on Sunday. The idea was to spoil the allies' finest hour and their triumphalist stance, recorded by CNN and the BBC, over the past few days. Briefly it worked.
Anti-Nato sentiment has been strong throughout Russia since the war's start but it was most intense in the military. The generals spotted the chance for some one-upmanship - but there were longer term consequences, not acknowledged. Not least was the undermining of Mr Ivanov, who had played a leading role in the Kosovo peace negotiations.
While he was telling the British Foreign Office yesterday that moving in the troops was "an unfortunate mistake" and that they would be withdrawn, Moscow's defence ministry officials were briefing Russian journalists that their deployment was not only deliberate but that the 200 men would stay.
And Itar-Tass in Belgrade was reporting that the operation had been co- ordinated with the Yugoslav leadership - a claim which, if true, might justify to Nato its reservations about Russian involvement in Kosovo. The embarrassed and now discredited Mr Ivanov surely did view the deployment as a mistake, but not so the generals.
Trust between the West and the Russians has been fraying steadily since the onset of the tough, chaotic post-Soviet years. After yesterday's events, with much unsettled business, including nuclear disarmament and non-proliferation, it seems to be hanging by a thread.
"We have been deceived, accidentally or deliberately," said a senior allied source. Among those with most cause for grievance is Mr Talbott and his team. He had been locked in talks with the Russian military for nearly 12 hours before hearing of the Russian advance.
For all Nato's efforts to play down the issue yesterday, the Russian entry into Kosovo was met with amazement and anger in Washington, London and Brussels. The White House demanded a detailed report; the British junior foreign minister, Doug Henderson, pretended Nato was unfazed, but the British swiftly protested to Moscow. And Mr Yeltsin's decision to hold an unscheduled morning meeting with his prime minister, chief- of-staff and foreign and defence ministers, suggests this was not a carefully planned operation in which he played the primary role. At home, Russia's stunt will be applauded but it has given the rest of the world more "proof" of the Kremlin's weakness; the breakdown in co-ordination between the defence ministry and foreign policy-makers is not seen as a symptom of strength.
Was it a rogue operation? The Pentagon yesterday said that US intelligence had intercepted orders from Moscow general staff to their paratroopers as they drove across Serbia. They were clearly told not to enter Kosovo, the Pentagon said. Were these instructions ignored or just altered later on?
The defence ministry was yesterday using the Russian news agency Interfax to insist that the operation was under the control of "the military leadership", though experiencing some "technical friction". The fact that a Russian general, Viktor Savazen - Moscow's former pointman at Nato, in Brussels - was quickly on the scene in Kosovo, suggests this is true.
But the ability of Russia's military to cause "disruption" in international affairs is a lesson that the west - and also Nato's K-FOR commanders in Kosovo - are unlikely to forget.