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Ethnic Albanian extremists, who are trying to drive Serbs out of Kosovo, have been blamed for the attack.
It took place near the town of Podujevo in northern Kosovo, 40km (25 miles) north-east of the capital Pristina.
The remote-controlled bomb was detonated 400m from the road at around noon, hitting the first of five buses which had just crossed the border into Kosovo from the city of Nis in Serbia.
Gorica Stjepanovic, 24, who survived the attack with eye injuries, said: "All of a sudden, everything burst, the bus seemed to have fallen apart.
"Blood was dripping from the roof. When I managed to get out, parts of bodies were everywhere."
The group of Serbs, who moved to Serbia fearing ethnic Albanian attacks, were travelling to the village of Gracanica in Kosovo to visit family graves.
The Orthodox Day of the Dead - 17 February - is when Serbs remember their dead.
The attack has sparked violent protests from the victims' relatives in Gracanica, who have blocked the main road into Pristina and set vehicles on fire.
The convoy was accompanied by five Swedish armoured vehicles which were unaffected.
Leaders of Kosovo's Albanian majority condemned the latest attack and said it was a serious blow to attempts to build peace.
Nato called the killings "premeditated murder".
Its Secretary General George Robertson said: "Nato did not conduct its air campaign in order to see ethnic cleansing by one group replaced by the ethnic attacks and intimidation of another."
The Yugoslav Government also condemned the attack and has declared a day of national mourning for the victims.
Earlier this week United Nations police came under attack in the town of Strpce after a Serbian man died while travelling in a UN convoy.
In March 1999, Nato launched air strikes against Yugoslavia following an escalation of violence against ethnic Albanians.
Almost three months later Belgrade agreed to a full military withdrawal from Kosovo.
It remains a province of Serbia - the main republic in Yugoslavia - but is now administered by the UN with troops from Nato, K-For, acting as a peacekeeping force.
Some ethnic Albanians want revenge for the atrocities committed by Serbian security forces under the rule of the now ousted Yugoslav President Slobodan Milosevic.
The attack is likely to further undermine efforts by the UN and K-For to improve relations between Serbs and ethnic Albanians and stop the violence.
The bomb attack happened as tension increased in Kosovo.
In the Presevo valley - part of a buffer zone keeping Yugoslav forces apart from K-For troops - there was violence between ethnic-Albanian separatists and Serbian forces.
In March 2004, 19 people were killed in the worst clashes between Serbs and ethnic Albanians since 1999, and Serb-owned homes and churches were attacked.
Many Serbs in Kosovo feel their community is dwindling and they are being forced out.
Ethnic Albanians number 1.5 million; some 80,000 Serbs remain following a post-war exodus of non-Albanians.
There have been signs of impatience on the part of the ethnic Albanian community over the length of time it is taking to decide Kosovo's future status.
The majority wants independence for the province, which is part of Serbia and Montenegro.
Ethnic Serbs would like Belgrade to take back control of the province.
In October 2004, they boycotted Kosovo's general election which was won by pro-independence ethnic Albanians.
Several rounds of UN-mediated talks have been held, without any significant breakthrough. The UN wants to find a solution for Kosovo's disputed status by the end of 2006.
The state union of Serbia and Montenegro is all that remains of the federation of six republics that made up former Yugoslavia - but in a referendum on 21 May 2006, Montenegro narrowly voted for independence from Serbia.
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