Armenian separatists in the breakaway region of Nagorny Karabakh said on Monday 15 more of its fighters have been killed in a flare-up of a territorial dispute, bringing the death toll to 39 as the fighting entered a second day.

World leaders have urged a halt to the fighting between Azerbaijan and the Armenian rebels after clashes erupted on Sunday, raising the spectre of an all-out conflict that could draw in regional powers — Russia and Turkey.

Ex-Soviet Armenia and Azerbaijan have been locked since the early 1990s in a territorial dispute over the Armenia-backed secessionist enclave, with deadly fighting flaring up earlier this year and in 2016.

The defence ministry in Karabakh announced a total military death toll of 32 on Monday. Seven civilian fatalities were reported earlier, including an Azerbaijani family of five and one woman and a child on the Armenian side.

The Armenian defence ministry said heavy fighting continued overnight and Monday morning along the frontline and claimed it had won back positions taken Sunday by Azerbaijani forces.

But Baku claimed further advances.

Azerbaijani forces "are striking enemy positions using rocket-artillery and aviation ... and have taken several strategic positions around the village of Talysh," the defence ministry said.

"The enemy is retreating," it added.

Martial law

Armenian military officials said Azerbaijani forces were continuing to attack rebel positions using heavy artillery, while Azerbaijan's defence ministry accused separatist forces of shelling civilian targets in the town of Terter.

Baku claimed to have killed 550 separatist troops, a report denied by Armenia.

The clashes erupted on Sunday morning with both sides accusing each other of initiating hostilities.

Fighting between Muslim Azerbaijan and majority-Christian Armenia threatened to embroil regional players Russia, which is in a military alliance with Yerevan, and Turkey, which backs Baku.

Armenia accused Turkey of meddling in the conflict and sending mercenaries to the battlefield.

France, Germany, Italy, the United States, the European Union and Russia have urged a ceasefire.

Armenia and Karabakh declared martial law and military mobilisation on Sunday, while Azerbaijan imposed military rule and a curfew in large cities.

Ethnic Armenian separatists seized the Nagorny Karabakh region from Baku in a 1990s war that claimed 30,000 lives.

Talks to resolve one of the worst conflicts to emerge from the 1991 collapse of the Soviet Union have been largely stalled since a 1994 ceasefire agreement.

France, Russia and the United States have mediated peace efforts as the "Minsk Group" but the last big push for a peace deal collapsed in 2010.