Azerbaijan President Ilham Aliyev last week immediately pardoned Ramil Safarov after he was extradited from Hungary, where he had been serving a life sentence for the 2004 killing.
Safarov was also promoted to the rank of major, given a house and eight years' worth of back-pay after returning home to a hero's welcome, in defiance of assurances from Baku to Budapest that he would serve out his term in Azerbaijan.
"We don't want a war, but if we have to, we will fight and win. We are not afraid of killers, even if they enjoy the protection of the head of state," Armenian President Serzh Sarkisian fumed in a statement late on Sunday.
Safarov hacked Armenian officer Gurgen Margarian to death at a military academy in Budapest where the servicemen were attending English-language courses organised by NATO.
His lawyers claimed in court that he was traumatised because some of his relatives had been killed during Azerbaijan's war with Armenia, and alleged that Margarian had insulted his country.
Armenia and Azerbaijan are locked in a long-running conflict over the disputed region of Nagorny Karabakh, where they fought a war in the 1990s.
Russia, which is part of the OSCE Minsk Group that is mediating in negotiations to find a peaceful solution to the Karabakh conflict, expressed "deep concern" over the extradition and pardon.
"We believe that these actions of the Azerbaijanis, as well as the Hungarian authorities, go against the efforts agreed at an international level primarily through the OSCE Minsk Group aimed at reducing tension in the region," Russian foreign ministry spokesman Alexander Lukashevich said in a statement.
The EU said Baku and Yerevan should refrain from exacerbating the dispute.
"We call on Azerbaijan and Armenia to exercise restraint on the ground and in public statements in order to prevent any kind of escalation of this situation," Maja Kocijancic, a spokeswoman for EU foreign policy chief Catherine Ashton, told a news conference in Brussels.
Yerevan on Friday cut diplomatic ties with Hungary over the pardon, while US President Barack Obama said he was "deeply concerned" about the incident.
Hungary summoned Azerbaijan's ambassador on Sunday to protest at Baku's decision after earlier saying it had been assured Safarov would serve out his term.
"Hungary finds it unacceptable and condemns the pardoning of Ramil Safarov," foreign ministry state secretary Zsolt Nemeth told ambassador Vilayat Guliyev, the national news agency MTI reported.
Armenia-backed separatists seized Nagorny Karabakh from Azerbaijan in the war that left some 30,000 people dead.
The two sides have not signed a final peace deal since the 1994 ceasefire and there are still regular firefights along the front line. Analysts warn the frozen conflict risks slipping again into full-scale war.
