Britain and Italy followed minutes later and Germany said it and a majority of European Union states would recognise a democratic Kosovo.
The smooth response Thaci had expected from the EU and the United States was tripped up earlier, when EU member Spain broke ranks to say "no".
Then U.S. President George W. Bush appeared to jump the gun ahead of his own State Department.
In a television interview during his tour of Africa, Bush said the people of Kosovo "are now independent". The remark was flashed in Kosovo as meaning U.S. recognition but White House spokeswoman Dana Perino said: "He didn't announce that."
"What he meant by that is that the Kosovars have declared their independence," Perino said, making clear it was the job of the U.S. State Department to officially declare recognition.
Bush was due to make a statement about Kosovo on Tuesday, in line with the original script which calls for the EU to go first in announcing its policy on what the West insists is a "European issue" that Serb ally Russia should not interfere in.
But the first word from Brussels had been a disappointment for Kosovo, though a ray of relief for Serbia.
"The government of Spain will not recognise the unilateral act proclaimed yesterday by the assembly of Kosovo," Foreign Minister Miguel Angel Moratinos told reporters.
"We will not recognise because we consider ... this does not respect international law," said the minister, whose country is grappling with separatist movements of its own.
Cyprus, Greece, Slovakia, Bulgaria and Romania have indicated they too are not keen to recognise Kosovo.
Afghanistan officially greeted the new Balkan state, but Vietnam and Azerbaijan said they would not recognise it. Kosovo confidently expects recognition from up to 100 other governments.
There was no shortage of protest by Serbs against the unilateral secession of the southern province, run by the United Nations and NATO for the past nine years.
Serbs protested against Kosovo's secession for a second day in Belgrade, in their Kosovo stronghold of Mitrovica, and in isolated Serb enclaves in central Kosovo. Several thousand turned out for the rallies, which remained peaceful.
Serbs in the Bosnian Serb capital Banja Luka also demonstrated, shouting "Kill the Albanians!" The EU appealed for calm after Serb nationalist protesters stoned Western
embassies in Belgrade on Sunday night.