Nato was not about to break apart, he told Serbs. It was growing stronger. Russia was not about to send squadrons of bombers to rescue Serbia. International public opinion had turned against Serbia after "horrible scenes of Albanian refugees and human suffering overwhelmed the Western world". Serbia must be ready to accept them back - and to accept a UN-led international "presence" in Kosovo.
Even for Yugoslav viewers, this was strong stuff. Was Mr Draskovic preparing himself to be the interlocuteur valable of Yugoslavia? The next president, perhaps?
Needless to say, Nato took what it wanted from Mr Draskovic's extraordinary soliloquy on the small Belgrade Studio B television channel, happy to quote his condemnation of government "lies" and his assertion that Nato is growing stronger - but equally content to censor out all his references to Nato's "aggression" against Yugoslavia and Nato's failure to obtain backing from the United Nations Security Council for its bombardment.
"Our people have been cheated by claims from the start that it's only a question of time before Nato breaks apart - that divisions are growing between Europe and the United States," Mr Draskovic said.
"Its aggression against the Federal Republic of Yugoslavia has enabled Nato to dominate Europe and to homogenise Nato itself. So Nato is becoming stronger. Romania and Bulgaria will enter Nato ... it may even become a kind of world military organisation. If Russia joins ... then it will be the greatest army in the world. So it is important that the UN places this machinery under international control."
The Secretary of State for Defence, George Robertson, quoted only the first and third sentences of this remarkable statement. And Nato leaders did not mention Mr Draskovic's demand that Albanian Kosovo refugees should return home with the help of world humanitarian organisations after "UN troops have come". But it was clear the Yugoslav Deputy Prime Minister was responding to the Nato summit in Washington, reminding his supporters that Yugoslavia was a founder member of the UN and that the UN covenant was little different to the constitution of Yugoslavia. The Rambouillet and Paris agreements had, in effect, provided for an independent Kosovo. That no longer applied.
But it was his implicit criticism of those around President Slobodan Milosevic that will have stung nationalist Serbs. "Many people talk about `unity' and `endurance'," he said. "But I believe the most important thing is to understand and get a grip on reality. The leaders of this country must clearly tell the people where we are and who we're with ... Will Nato break apart? Some false prophets claim that in a couple of days we will celebrate victory over Nato. They must tell us what is the world public opinion ... Let's not lie to the people any more that we are getting the Russian Sukhoi [bomber], or S-300s or S-400s or military aid or that Russia is entering World War Three."
World opinion supported Yugoslavia in the first week of the Nato bombardment, Mr Draskovic said, but the sight of human suffering among the Albanian refugees had turned the world "almost entirely against us - but this is concealed here". Western countries were "mainly reasonable and moderate". Words were being misused. Why did the state media refer to "criminal Nato aggression" as if aggression could ever be anything but criminal?
"The other night, someone said [on television] that the three Nato PoWs should have been taken to Branko's Bridge [in Belgrade] and roasted there on a spit. I protested about this in the federal government - although I'm willing to defend the media's freedom, I demanded that these people be taken off the television because they shame Serbia and our tradition. Serbs do not roast people."
There can be little doubt that several leading figures in the regime will feel like roasting Mr Draskovic for his remarks. The leader of the democratic movement a couple of years ago,the Deputy Prime Minister is regarded by many as a turncoat for joining the Milosevic coalition. He didn't cry surrender yesterday. He didn't call for the overthrow of the regime. The "cracks" in the government to which Mr Robertson referred had been there all along. But his words just might provide a political path out of a war that neither side seems able to win.