The worst clashes in years over the disputed Armenian enclave of Nagorno-Karabakh in Azerbaijan have left 15 soldiers dead in recent days.
Azerbaijan says 12 of its troops were killed in the past four days while the enclave's ethnic Armenian authorities say three of their soldiers died.
Armenia says the presidents of the two countries are to meet next week to try to calm the situation.
A ceasefire was agreed 20 years ago after 30,000 deaths over six years.
The two sides blame each other for violating the ceasefire since then.
International attempts to revive the peace process stalled recently and both Azerbaijan and Armenia have been using increasingly militant rhetoric regarding the dispute, Konul Khalilova of the BBC's Azeri service says.
Every year, hundreds of people, including many civilians, die along the Line of Contact between Nagorno-Karabakh and Azerbaijan as the result of skirmishes and sniper fire, she adds.
Armenia's Prime Minister, Hovik Abrahamyan, announced late on Saturday that President Serzh Sargsyan of Armenia would meet his Azerbaijani counterpart, Ilham Aliyev, in the Russian Black Sea resort of Sochi next Friday or Saturday.
Russia, which brokered the 1994 ceasefire, said in a statement on its foreign ministry's website (in Russian): "We see the events of recent days as a serious violation of agreements on a ceasefire and declared intentions to achieve a regulation through political means.
"We take the position that any further escalation is unacceptable."
The US co-chair of the Organization for Security and Cooperation in Europe (OSCE) Minsk Group, which works to resolve the dispute, expressed concern over the violence on Friday.
"We are seriously concerned about the recent upsurge in violence along the line of contact," James Warlick said in a tweet. "The ceasefire needs to be respected."