Last week Hungary released soldier Ramil Safarov to Baku, where Azeri President Ilham Aliyev pardoned him on arrival. Safarov had served eight years of his life sentence for killing an Armenian officer during a NATO training in Hungary.
Armenia immediately broke diplomatic ties with Hungary and said releasing Safarov, who was given a hero's welcome on his return, was a "grave mistake".
Armenia and Azerbaijan have been at odds since the war between ethnic Azeris and Armenians that erupted in 1991 over the mainly Armenian Nagorno-Karabakh enclave. A ceasefire was signed in 1994 but new cross-border clashes this year have prompted worries of a resumption of fighting.
Hungary said it acted in compliance with international law and that Azerbaijan had promised to uphold Safarov's sentence. While the two countries were in talks about developing closer economic ties, these were in no way linked to the release of the soldier, it said.
Azerbaijan dismissed media reports that it planned to buy Hungarian bonds, which blogs and newspapers had speculated might have played a part in Safarov's release.
Protesters chanting "We are sorry, Armenia" said they doubted the government's motives, adding that whatever the reasons, the decision was unacceptable.
"Murderers should not be extradited to countries where it is clear that ethnic hate crimes are considered heroism," said protester Laszlo Muhari, 30. "In a democratic country this is not acceptable."
"(Prime Minister Viktor) Orban should stop lying and start giving clear answers, because it is simply impossible that such a brutal killer is just released without a background deal."
