Moscow on Thursday called for "restraint" following a new escalation in fighting between Armenia and Azerbaijan over the disputed Nagorno-Karabakh region that has left three people dead.

Earlier in the day Armenian Prime Minister Nikol Pashinyan voiced rare criticism of ally Moscow, questioning the work of Russian peacekeepers in Nagorno-Karabakh.

"We express our extreme concern over the escalation of tensions," the Russian foreign ministry said in a statement, calling on all parties "to exercise restraint and observe a ceasefire".

The foreign ministry added that Moscow's peacekeepers were "making every effort" to stabilise the situation on the ground.

The former Soviet republics of Armenia and Azerbaijan have fought two wars -- in the 1990s and in 2020 -- over Nagorno-Karabakh.

In the aftermath of the latest war, Armenia ceded swathes of territory it had controlled for decades.

Russia deployed some 2,000 peacekeepers to oversee the fragile truce but tensions persist despite the ceasefire agreement.

Following the recent flareup, Pashinyan questioned the role of Russian peacekeepers there.

"Questions arise in Armenian society over the Russian peacekeeping operation in Nagorno-Karabakh," he told a government meeting on Thursday.

He pointed to "gross, prolonged violations of a ceasefire regime" and "constant physical and psychological terror" of Karabakh residents in the presence of the peacekeepers.

Pashinyan said the role of the Russian peacekeeping mission must be "clarified", adding that Armenia expected the contingent to prevent "any attempt to violate the line of contact".

The two sides accuse each other of violating the fragile truce.

On Wednesday, Baku said it had lost a soldier and the Karabakh army said two of its troops had been killed. Pashinyan said 19 troops had been wounded.

The Azeri defence ministry said Karabakh troops targeted its army positions in the district of Lachin, which is under the supervision of the Russian peacekeeping force.

The Azeri army later said it conducted an operation dubbed "Revenge" in response and took control of several strategic positions.

On Friday, Russian President Vladimir Putin is hosting Turkish President Recep Tayyip Erdogan for talks in the Black Sea resort city of Sochi.

Turkey backed Azerbaijan in the 2020 war over Karabakh.