Armenia declared a national mobilisation to “defend our sacred homeland” after fierce fighting involving tanks, aircraft and artillery broke out with Azerbaijan forces on Sunday.
In the latest flare-up of a decades-long conflict over the disputed Nagorno-Karabakh region, Azerbaijan said it had captured seven of its Armenian-controlled villages, a claim Yerevan denied.
Armenia said Azerbaijan started bombarding along the contact line separating the two forces and shelled civilians including in the region’s capital, Stepanakert.
Armenian Prime Minister Nikol Pashinyan declared martial law and ordered a general mobilisation after Azerbaijan's “pre-planned aggression".
Azerbaijan's Defence Ministry denied that it started the fighting.
Azeri President Ilham Aliyev said in a state TV address that: "We'll win as our cause is just."
France, Russia and others urged calm after the latest flare-up over Nagorno-Karabakh.
Fighting has repeatedly broken out there since Armenia took control of the territory and seven surrounding districts from Azerbaijan in a war after the Soviet Union collapsed in 1991.
Hundreds were killed in a five-day war in 2016 before Russia pressured both sides to resume a ceasefire that was first brokered in 1994.
Despite decades of mediation by the US, France and Russia, no peace agreement has been signed.
Russia again called on both sides to halt fighting immediately and to return to negotiations to ease tension, the Foreign Ministry in Moscow said.
France called on Yerevan and Baku to end hostilities and immediately restart dialogue.
"France is extremely concerned by the confrontation," Foreign Ministry spokeswoman Agnes von der Muhll said.
The EU also called for a halt in fighting.
"Military action must stop, as a matter of urgency, to prevent a further escalation," European Council president Charles Michel tweeted.
Mr Michel called for "an immediate return to negotiations, without preconditions".
Pope Francis appealed to Armenia and Azerbaijan on Sunday to resolve their differences through negotiations.
"I pray for peace in the Caucasus and ask the parties in conflict to make concrete gestures of goodwill and brotherhood that can lead to the resolution of problems, not with the use of force and weapons but through dialogue and negotiations," the Pope said.
Turkey will stand by its ally Azerbaijan “with all our means until the end", Turkish Defence Minister Hulusi Akar said, without elaborating.
The Azeri army is using tanks, artillery, missile systems and aircraft against Armenian positions near the front line and deeper into Armenian-held territory, the Defence Ministry in Baku said.
As many as 12 Armenian anti-aircraft systems have been destroyed and one Azeri helicopter was shot down, it said.
Armenian forces hit two Azeri helicopters, three tanks and 14 drones, Armenian Defence Ministry spokeswoman Shushan Stepanyan said.
Civilians in Nagorno-Karabakh have been urged to go into shelters after Azerbaijan shelled Stepanakert, said Vahram Poghosyan, a presidential spokesman.
“Our response will be proportional and full responsibility is on the military-political leadership of Azerbaijan,” Mr Poghosyan said.
An Armenian woman and child were killed, although the full toll is unclear.
About 10 Armenian servicemen have been killed in the fighting, Samvel Babayan, secretary of the Nagorno-Karabakh Security Council, told Radio Liberty.
Armenia last week said Mr Aliyev was preparing for war after he claimed Armenia was massing forces near Nagorno-Karabakh for a new war.
As the fighting raged, Facebook and other social media appeared blocked in Azerbaijan and internet access was slow in some areas.