File Photo: Armenian wounded soldier getting treatment at the basement of a medical center outside the city of Stepanakert, during the ongoing fighting between Armenia and Azerbaijan over the disputed region, on October 14, 2020. AFP
The ex-Soviet Caucasus neighbours fought last autumn a six-week war over the contested region of Nagorno-Karabakh which has claimed more than 6,500 lives.
Hostilities ended last November with a Russian-brokered ceasefire under which Yerevan ceded swathes of territory it had controlled for decades.
Baku's defence ministry said an Azerbaijani soldier "was killed overnight as a result of a provocation by Armenia's armed forces" near the countries' shared border.
"Full responsibility for the escalation lies with Armenia's political and military leaders," the ministry said in a statement.
Armenia, meanwhile, said Baku had opened fire on its positions on Wednesday night on the eastern part of their shared border.
It called on Azerbaijan to "refrain from provocative actions."
Armenian Prime Minister Nikol Pashinyan and Azerbaijani President Ilham Aliyev met for rare face-to-face talks under the mediation of Russian President Vladimir Putin last month.
The talks focused on resolving disputes left over from last year's war, and were hailed by all sides as positive.
The trio met less than two weeks after the worst fighting since the Karabakh war killed six Armenian troops and seven Azerbaijani soldiers.
They discussed demarcation issues between the two Caucasus countries, as Yerevan accuses Baku's forces of intruding into its sovereignty territory.
They also addressed the issue of rebuilding Soviet-era transport links between Azerbaijan and Armenia which are currently closed by a mutual blockade.
On December 4, Azerbaijan freed 10 Armenian soldiers it had captured during border clashes last month.
Aliyev and Pashinyan are to meet again in Brussels on December 15 for talks mediated by the European Council President Charles Michel.
Ethnic Armenian separatists in Nagorno-Karabakh broke away from Azerbaijan as the Soviet Union collapsed in 1991, and an ensuing conflict claimed around 30,000 lives.