Armenia, which claims Azerbaijan launched an air and artillery attack, has declared martial law and called for total mobilization of the male population.
Azerbaijan in turn said it was responding to shelling along the whole front. Both sides have reported civilian deaths.
Russia also weighed in on Sunday and called for an immediate ceasefire and for talks in order to stabilize the region.
Armenia and Azerbaijan were part of the Soviet Union before its collapse in 1991 and have since then been embroiled in an unresolved dispute over the region.
Nagorno-Karabakh is internationally recognized as part of Azerbaijan but it is controlled by ethnic Armenians.
Heavy fighting between the two countries erupted on Sunday, as they blamed each other for the escalation that led to reports of casualties.
Armenia’s ministry of defense said its forces downed two Azerbaijani helicopters and three drones in response to an attack it said began at 04:10 GMT.
But Azerbaijan’s defense ministry said it launched a “counteroffensive to suppress Armenia’s combat activity and ensure the safety of the population”, using tanks, artillery missiles, combat aviation and drones.
The ministry said an Azerbaijani helicopter had been downed but its crew had survived.
“There are reports of dead and wounded among civilians and military servicemen,” Hikmet Hajiyev, spokesman for the Azerbaijani presidency, said in a statement.
In a statement on Facebook, Armenian Prime Minister Nikol Pashinyan said “the government has decided to declare martial law and a total mobilization”, telling citizens to “get ready to defend our sacred homeland”.
Azerbaijani President Ilham Aliyev, meanwhile, said in a televised address to the nation that “there are losses among the Azerbaijani forces and the civilian population as a result of the Armenian bombardment”.
He warned that those using intimidation tactics against his country would regret it, adding that Azerbaijan defends its lands and Nagorno-Karabakh belongs to it.
Al-Jazeera reported that in Nagorno-Karabakh officials also declared martial law and ordered citizens to mobilize. The region’s ombudsman Artak Beglaryan said “there are civilian casualties” among the population in the region.
Meanwhile, Turkish Defense Minister Huluzi Akar told Anadolu News Agency that the “biggest obstacle to peace and stability in the Caucasus is the hostile stance of Armenia and it must immediately turn back from this hostility that will send the region into fire.”
Turkey’s Defence Minister Hulusi Akar said on Sunday that Ankara would support Azerbaijan with “all its resources”.
There was no immediate reaction to Turkey’s comments from Armenia.