Amnesty says rival sides attacked civilians, as it called on both countries to investigate use of ‘inaccurate’ weapons.
Armenia has said one of its soldiers was killed in a border shoot-out with Azerbaijani forces, with tensions still high after last September’s war over the disputed Nagorno-Karabakh region.
Armenia’s Ministry of Defence said on Tuesday that the shoot-out took place on its eastern border with Azerbaijan.
It later said the situation was “calm” after a skirmish at the Verin Shorzha border point in Armenia’s eastern Gegharkunik district.
“One serviceman has been killed as a result of a shootout that followed the opening of fire by Azerbaijani troops,” the ministry said in a statement.
Later on Tuesday, Azerbaijan’s Ministry of Defence denied accusations by Armenia that it had fired across the border at Armenian positions.
“According to our information, the incident involving the death of an Armenian soldier was an accident and it has nothing to do with the Azerbaijani side,” Azerbaijan’s ministry said in a statement, adding that it was in contact with the Russian side on the issue.
A long-simmering conflict over Nagorno-Karabakh erupted into full-blown war in late September, with some 6,000 people killed in six weeks of fighting.
Russia helped to secure a ceasefire in November after Azeri troops drove ethnic Armenians out of territory they had controlled since the 1990s in and around the Nagorno-Karabakh region.
Russia, which has a military base in Armenia, sent peacekeepers to the area last year to help enforce the ceasefire.
It has strong ties and a mutual defence pact with Armenia but is also friendly with Azerbaijan.
The ceasefire, monitored by some 2,000 Russian peacekeepers, has largely held but tensions have continued and there have been several border incidents.
Earlier this month, Armenia accused Azerbaijan’s military of crossing the southern border in an “infiltration” to “lay siege” to a lake that is shared by the two countries.