The Burundian army said that Papal nuncio Michael Courtney was ambushed by National Liberation Forces (FNL) rebels and shot three times on Monday.
"The nuncio was ambushed this afternoon by elements of the FNL near the Minago locality 40km south of Bujumbura," army spokesman Augustin Nzabampema said.
The 58-year-old Irishman died in hospital while undergoing surgery.
However, the rebel FNL condemned the murder and said it was not involved in the incident.
"We have nothing against the nuncio. We have men in the area where he was ambushed, but I swear it wasn't us who attacked him," rebel spokesman Pasteur Habimana said.
Courtney was travelling in a diplomatic car flying the Vatican flag when he was attacked, the army said.
Two other passengers in the car, both Burundian, escaped the ambush uninjured.
"They deliberately killed him, but we do not know the reason," the army spokesman said.
"The nuncio received three bullets, one in the head behind the right ear, another in the thorax and a third in the right
leg," said Tharcisse Nzeyimana, a senior official at the Prince Louis Clinic in Bujumbura.
"We tried to resuscitate him and give him a transfusion, but his condition was serious and he succumbed to his injuries."
A Burundian clergyman said Courtney, who had lived in Burundi for three years, was returning from a funeral for a priest in Minago.
Courtney was due to leave for Cuba for another assignment in the next few weeks, the clergyman added.
The Vatican issued a statement saying Pope John Paul was praying for Courtney's soul.
In New York, UN Secretary-General Kofi Annan expressed his shock and sadness at Courtney's murder.
"The secretary general recognised the quiet and effective manner in which the monsignor had been helping the peace process in Burundi
"The secretary general recognised the quiet and effective manner in which the monsignor had been helping the peace process in Burundi," said UN spokesman Fred Eckhard.
Annan expressed the hope that the perpetrators of Courtney's murder would be brought to justice, and offered his condolences to family members and to Pope John Paul.
Burundian President Domitien Ndayizeye also condemned the attack on Courtney.
"The people who committed the attack are enemies of peace in Burundi," Ndayizeye said in radio and television broadcasts, identifying the region where the attack took place as an FNL stronghold.
Burundi has been in the throes of a decade-old civil war, with the majority Hutu ethnic group fighting to end the political dominance of the Tutsi minority.
More than 300,000 people have been killed in the fighting.
The government and the main rebel group, the FDD (Forces for the Defence of Democracy), agreed in October to share power.
The government has since awarded top ministerial and
military posts to rebel leaders.
But the FNL has refused to negotiate with the government and has continued to attack the capital, Bujumbura.