Two other BBC staff were lightly wounded in the attack Wednesday.
BBC radio reporter John Schofield, 29, was shot and killed immediately by a single bullet through the neck.
Adam Kelleher, a British cameraman, suffered a ricochet wound in the wrist, and Omar Asawi of the television Arabic service was hit by a ricochet shot in the leg. Briton Jonathan Birchall of the World Service was not hurt.
Croatian officials blamed rebel Serbs for the attack and said the journalists were in the area illegally.
Traveling in a relief convoy toward Bihac, the BBC journalists were filming when they came under sustained small arms fire from the Croatian army, the British Broadcasting Corp. said Wednesday in London.
In Zagreb, UN spokesman Chris Gunness said Thursday the crew told him they were filming houses being torched. There was firing. The crew lay on the ground, and Schofield was shot in the neck.
Croatian soldiers then suddenly appeared and "actually apologized'' for the shooting, Gunness said.
"The belief is ... that the shot came from quite close range ... which calls for further investigation,'' he said.
The British Embassy in Zagreb said Schofield's body had been retrieved by the Croatian army early Thursday and was being transported to a Zagreb morgue.
The two wounded journalists were released Thursday from the hospital where they were treated with minor injuries. They briefed British Ambassador Gavin Hewitt on the incident, an Embassy official said.
"Our first priority is to repatriate the body as soon as possible,'' the official, who asked not to be identified, said. She said Hewitt communicated on the "highest level'' with the Croatian government and was promised an investigation into the incident.
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