Nagorno-Karabakh, which lies inside Azerbaijan but is controlled by ethnic Armenians, has run its own affairs with heavy military and financial backing from Armenia since a separatist war ended in 1994.
Azerbaijan frequently threatens to take Nagorno-Karabakh region back by force. Clashes around the region have fueled worries of a widening conflict breaking out in the region, which is crossed by oil and gas pipelines.
Both sides report numerous casualties, accusing each other on Saturday of violating a ceasefire, a sign that the two-decade-old conflict which has left some 30,000 people dead is far from a peaceful resolution.
Similar violence was reported last month.
"The enemy, using tanks, artillery and aviation made attempts to get deep into the defense lines of the Nagorno-Karabakh Army of Defense and capture tactical positions. The enemy was thwarted," the Armenian Defense Ministry said in a statement.
The wave of violence has forced Russia, a key mediator in the conflict, to step up diplomatic efforts to quench it.
Russia's President Vladimir Putin has urged both sides to observe an immediate ceasefire and "to exercise restraint so as to avert new human casualties," Kremlin spokesman Dmitry Peskov said, Reuters reported.
Russian Foreign Minister Sergei Lavrov and Defense Minister Sergei Shoigu have talked by phone with their Armenian and Azeri counterparts.
Lavrov has called on them to "deal with the situation to stop the violence", while Shoigu called for "immediate measures to stabilize the situation in the conflict zone".
War erupted over Nagorno-Karabakh in dying years of the Soviet Union, and killed about 30,000 people. A ceasefire was called in 1994 but violence has sporadically broken out since.
On Wednesday, US Secretary of State John Kerry called for "an ultimate resolution" of the conflict between during talks with Azeri President Ilham Aliyev at the State Department.