PRISTINA, Serbia-Thousands of wildly cheering pro-independence demonstrators marched through Kosovo's gritty capital Monday as a sense of euphoria swept the breakaway province preparing to gain statehood early next year.

Giddy Kosovars, assured of staunch U.S. support and a promise of recognition from all but one EU country, reveled in hopes that a decades-old dream may finally be within reach despite fierce opposition by Serbia and Russia.

"Independence means so much to us. It means a new identity and a new future for Kosovo," said Agim Kastrati, a 19-year-old law student who marched through Pristina demanding a declaration of statehood early in 2008.

European Union foreign ministers meeting Monday in Brussels, Belgium, said they had "virtual unanimity" on recognizing Kosovo's eventual independence, with Cyprus the sole holdout.

And Kosovo's outgoing prime minister demanded an "immediate and permanent" conclusion to the ethnic Albanian majority's drive for statehood, a quest that led to the 1998-99 war with Serbia and spawned nearly a decade of political and economic limbo under U.N. and NATO administration.

"No more delays. No more deals," said rally organizer Burim Balaj, as 3,000 demonstrators outside parliament set off firecrackers, waved U.S. and Albanian flags and held posters that read: "Independence is the only option."

"UCK! UCK!" the crowd shouted back, using the Albanian acronym for the now-disbanded Kosovo Liberation Army, or KLA, which fought Slobodan Milosevic's troops in a conflict that claimed 10,000 lives.

Yet the celebratory mood was tinged with uncertainty. Some wondered whether the seemingly imminent birth of a nation will re-ignite ancient ethnic hatreds and thrust the Balkans into a new cycle of bloodshed.

NATO, which maintains 16,000 peacekeepers in Kosovo, has boosted street patrols in a show of force aimed at discouraging extremists on both sides of the ethnic divide.

"I don't believe it's possible for Serbs and Albanians to live together peacefully," said Mimoza Sejdiu, 24, an ethnic Albanian at Monday's rally. "I don't see a common future as citizens of one country."

In a sign of underlying tensions, Kosovo police said that over the weekend, unknown assailants tossed a bottle of flaming liquid into a vacant house owned by Serbs in the town of Gnjilane southeast of Pristina and sprayed this menacing message: "Death to Serbs."

Former KLA rebels are believed to have stashed away huge caches of rocket-propelled grenades and other weapons in Kosovo's forests and in their own backyards. More than 500,000 handguns alone remain in circulation, according to U.N. estimates.

Serbia, which has offered Kosovo broad autonomy but insists the province remain part of its territory, has threatened economic blockades, and some officials have even hinted that Belgrade might resort to force to retain what many Serbs see as the cradle of their civilization.

In a provocative move seen as a fresh territorial claim, Serbia's minister for Kosovo, Slobodan Samardzic, opened a branch office in the ethnically divided northern city of Kosovska Mitrovica, long a flashpoint for violence.

Russia, Serbia's No. 1 ally, has threatened to veto any move by the U.N. Security Council to sign off on statehood. Moscow contends independence for Kosovo would encourage separatists in Chechnya, Georgia and elsewhere to break away.

"This will trigger a chain reaction in the Balkans and in other areas of the world," Russian Foreign Minister Sergey Lavrov warned Monday during a visit to Cyprus, itself a divided nation.

But Washington signaled anew that it was ready to recognize an independent Kosovo, raising the likelihood of a showdown when the Security Council takes up the issue on Dec. 19.

"Over the next few weeks, the United States will work closely with our international partners to resolve this issue. The people of Kosovo and the region urgently need clarity about their future," U.S. State Department spokesman Gonzalo Gallegos in a statement.

In the past four months of talks, negotiators from the U.S., EU and Russia explored "every realistic option for an agreement and, in their words, 'left no stone unturned' in the search for a mutually-acceptable outcome," Gallegos said.

Although Kosovo's leaders have vowed not to declare independence without U.S. and European Union approval, government spokesman Skender Hyseni said a declaration was "not an issue of if, but when."

Officials suggested it would come sometime in January or February. That would start a 120-day internationally supervised transition, during which the U.S. and other countries would recognize the new state and the U.N. would hand off administration to the EU.

In an interview with The Associated Press, outgoing Prime Minister Agim Ceku pledged "our commitment to multi-ethnicity, our commitment to democracy, our commitment to international supervision of independence, our commitment to international partnership and our commitment to a European future."

"Serbia has a choice: Going into the future together with us, or going back to the past alone. We hope that they will make the right choice," said Ceku, who is preparing to hand over power to former rebel leader Hashim Thaci.

Diplomats said recognition likely would come in waves, with the U.S. and key European powers such as Britain, France, Germany and Italy among the first. The Baltic countries and Scandinavia would be in a second wave, and most of the rest of the 27-nation bloc would follow in a third wave, officials said.

In Brussels, British Foreign Secretary David Miliband said the EU must find unity fast.

"Kosovo is in Europe's backyard, and it's absolutely vital that there is a strong European commitment," he said.