A new wave of fighting broke out in the Nagorno-Karabakh region on Saturday, killing dozens and drawing international calls for an immediate ceasefire to stop violence spreading in the South Caucasus.

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.

The Azeri defense ministry said on Saturday the army had "liberated strategic heights and settlements" in the region.

"Six Armenian tanks were destroyed (and) more than 100 Armenian servicemen were killed and injured," it said in a statement, saying 12 Azeri servicemen had also been killed.

Armenia's government denied the Azeri report on the number of casualties. Armenian President Serzh Sarksyan told a State Security Council meeting about 18 were killed and 35 injured. It was not immediately clear if the death toll included soldiers only.

Earlier on Saturday, Nagorno-Karabakh's military said Armenian anti-aircraft forces had downed an Azeri helicopter. Baku admitted that its Mi-24 helicopter was shot down.

Both sides also reported civilian casualties and accused each other of violating a 1994 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.

Armenia is historically Christian, while Azerbaijan is traditionally Muslim.

The violence has forced Russia, a key mediator in the conflict, to step up diplomatic efforts to quench it.

President Vladimir Putin urged the warring sides to immediately observe the ceasefire and "to exercise restraint so as to avert new human casualties," Kremlin spokesman Dmitry Peskov was quoted as saying by the Interfax news agency.

Russian Foreign Minister Sergei Lavrov and Defense Minister Sergei Shoigu have talked by phone with their Armenian and Azeri counterparts.

German Foreign Minister Frank-Walter Steinmeier, meanwhile, called on both sides "to immediately stop fighting and to fully respect the ceasefire."

Azerbaijan frequently threatens to take Nagorno-Karabakh 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 natural gas pipelines.

On Wednesday, U.S. 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.