At least 11 troops and a civilian were killed on Tuesday in a third day of fighting between Azerbaijan and Armenia, despite international calls for restraint.

The fighting between the arch-foes in the South Caucasus since Sunday is the heaviest in years, raising fears of a major flare-up in the volatile region.

All-out war between the ex-Soviet republics could have wider implications and pit regional rivals Russia and Turkey against each other.

Azerbaijan said seven of its troops -- including a major general and a colonel -- and a civilian had died on Tuesday, and Armenia said four of its troops had been killed, its first reported fatalities in the clashes.

Overall, 16 people have been killed from both sides since Sunday.

The ex-Soviet republics have for decades been locked in a simmering conflict over Azerbaijan's southwestern separatist region of Nagorny Karabakh, which was seized by ethnic Armenian separatists in a 1990s war that claimed 30,000 lives.

Fighting outside the region is rare, but since Sunday the two sides have reported clashes in northern areas along their shared border.

The fighting hundreds of kilometres from Nagorny Karabakh has prompted calls for an immediate ceasefire from the United States, European Union and the regional power broker Russia.

Azerbaijan's defence ministry said Armenian forces had attacked its positions in the northern Tovuz region with artillery fire, mortars and large-calibre machine-guns on Tuesday. It said several villages in the area had also come under fire.

Azerbaijani forces opened fire again on the northeastern section of the border in its Tavush province, the defence ministry spokesman, Sushan Stepanyan, said.

Azerbaijan's ally Turkey -- which competes with Russia for the influence in the strategic region -- expressed support for Baku.

Turkish foreign ministry has accused Armenia of "aggressive nationalism" and vowed to "continue, with all its capacity, to stand by Azerbaijan in its struggle to protect its territorial integrity."

Clashes on Armenia-Azerbaijan border
Clashes on Armenia-Azerbaijan border AFP / STAFF

Azerbaijani political analyst Elhan Shahinoglu said the probability of a full-scale war was now "very high".

"An Azerbaijani general has been killed and Baku will retaliate," he said.

"There is a widespread popular demand in Azerbaijan to shift military actions to Karabakh."

But Armenian analyst Hakob Badalyan said an all-out war was very unlikely.

"Baku and Yerevan, as well as the region's geopolitical powers (Russia and Turkey), don't want a big war which they know will lead to catastrophic consequences," he said, adding that neither side was in a clear position to win a protracted conflict.

Four years ago, Azerbaijan had military superiority over its neighbour, but Armenia has since "restored the balance" with purchases of sophisticated Russian weapons, he said.

In April 2016, four days of fierce fighting in Karabakh -- the worst violence in decades -- claimed dozens of lives from both sides and nearly spiralled into full-scale war.

Mediated by the "Minsk Group" of diplomats from France, Russia and the United States, talks on the Karabakh conflict have been largely stalled since a 1994 ceasefire deal.

Armenia, which controls the disputed region, is happy with the status quo in Karabakh that also suits Russia's interests as the Kremlin uses its power-broker's role in asserting its influence in the ex-Soviet republics.

Moscow has a military alliance with Armenia, where it maintains a base, but supplies both Yerevan and Baku with weapons worth billions of dollars.

Energy-rich Azerbaijan, whose military spending exceeds Armenia's entire state budget, has repeatedly threatened to restore control over the territory by force.

Armenia has vowed to crush any military offensive.