US President George W Bush has said history will prove the independence of Kosovo to be justified.
In a speech in Tanzania, Mr Bush said the US would soon establish full diplomatic relations with Kosovo.
Serbia earlier withdrew its envoy to Washington in protest. It says Kosovo's declaration of independence on Sunday violates international law.
The UN Security Council is divided over how to respond to Kosovo's move, and it has failed to agree any action.
Russia and China supported Serbian President Boris Tadic when he made an impassioned appeal to the Council at Tuesday's meeting.
But Britain's representative said that with no prospect of agreement between Belgrade and Pristina the only way forward was supervised independence for Kosovo.
Britain, France, Germany and Italy have all recognised the new state but others have not.
In his speech, Mr Bush said there was "a disagreement but we believe as many other nations do that history will prove this to be the correct move".
STANCE ON RECOGNITION
For: Germany, Italy, France, UK, Austria, US, Turkey, Albania, Afghanistan
Against: Russia, Spain, Romania, Slovakia, Cyprus
The president, who was speaking during a tour of Africa, said the US supported Kosovo's independence because "we believe it will bring peace".
Earlier, in a letter to Kosovo's President Fatmir Sejdiu, Mr Bush offered friendship to Kosovo, and said he supported "your embrace of multi-ethnicity as a principle of good governance".
On Monday, the Serbian parliament passed a resolution condemning Kosovo's declaration of independence.
The resolution also formally annulled the acts of the government in Pristina, saying Belgrade's sovereignty over Kosovo was guaranteed by the UN and international law.
In a separate move, Serbia recalled its ambassadors to the US, France and Turkey because those countries had recognised Kosovo's independence.
Serbian Prime Minister Vojislav Kostunica has threatened to withdraw envoys from other countries which backed the territory's secession.
At a meeting in Brussels, the European Union set aside differences over the recognition of Kosovo's independence, by stressing that the breakaway Serbian province was not a precedent for separatists elsewhere.
All 27 EU foreign ministers agreed to leave recognition up to each member state.
Spain and several other member states have withheld recognition because of concerns about separatist movements within their own borders.
Serbia's interior ministry has filed criminal charges against Kosovo Albanian leaders instrumental in proclaiming independence, accusing them of proclaiming a "false state" on Serbian territory.
HAVE YOUR SAY
Kosovo has declared independence from Serbia, legally or illegally it is not for me to say which
In Belgrade, about 10,000 students marched in protest at the independence declaration, and Serb enclaves inside Kosovo also saw big anti-independence rallies.
In Kosovo's divided city of Mitrovica, three cars were damaged in Tuesday's grenade attack near the office of the Organisation for Security and Co-operation in Europe.
The incident was the latest in a string of hand-grenade attacks on property of international missions in Kosovo and government offices.
Serbian security forces were driven out of Kosovo in 1999 after a Nato bombing campaign aimed at halting the violent repression of ethnic Albanian separatists.
The province has been under UN administration and Nato protection since then.