The conflict has reignited concerns about stability in the South Caucasus region, a corridor for pipelines carrying oil and gas to world markets
Armenia and Azerbaijan accused one another on Tuesday of firing directly into each other's territory and rejected pressure to hold peace talks as their conflict over the enclave of Nagorno-Karabakh threatened to mushroom into all-out war.
Both reported firing from the other side across their shared border, well to the west of the breakaway Nagorno-Karabakh region over which fierce fighting broke out between Azeri and ethnic Armenian forces on Sunday.
The incidents signalled a further escalation of the conflict despite urgent appeals from Russia, the United States and others to halt it.
The conflict has reignited concerns about stability in the South Caucasus region, a corridor for pipelines carrying oil and gas to world markets.
Azeri President Ilham Aliyev, speaking to Russian state television, flatly ruled out any possibility of talks. Armenian Prime Minister Nikol Pashinyan told the same channel they could not take place while fighting continued.
Nagorno-Karabakh is a breakaway region inside Azerbaijan but run by ethnic Armenians and backed by Armenia. It broke away from Azerbaijan in a 1990s war but is not recognised by any country as an independent republic.
Dozens of people have been reported killed and hundreds wounded since clashes between Azerbaijan and ethnic Armenian forces broke out on Sunday, threatening to draw in neighbours including Azerbaijan's close ally Turkey.
After a closed-door discussion on Tuesday the 15-member U.N. Security Council "expressed concern" about the clashes, condemned the use of force and backed a call by U.N. Secretary-General Antonio Guterres for an immediate halt to fighting.
Further stoking tensions between the two former Soviet republics, Armenia said a Turkish F-16 fighter jet had shot down one of its warplanes over Armenian airspace, killing the pilot.
It provided no evidence of the incident. Turkey called the claim "absolutely untrue", and Azerbaijan also denied it.
"The international community should decisively condemn the aggression of Azerbaijan and the actions of Turkey and demand Turkey get out of this region," Pashinyan told Russian state TV.
"The military presence of Turkey in this region...will bring further escalation and expansion of the scale of the conflict."
Azeri leader Aliyev accused Armenia of fabricating the plane incident. "Turkey is not a party to the conflict, in no way participates in it and there is no need for this," he said.
Aliyev said Azerbaijan was calling up tens of thousands of reservists under a partial mobilisation announced on Monday.
"We are able to punish the aggressor ourselves so that he would not even dare to look in our direction," he said.
Any descent into all-out war could threaten to drag in not only Turkey, but Russia. Moscow has a defence alliance with Armenia, but also enjoys close relations with Azerbaijan.
The Kremlin said President Vladimir Putin spoke by phone to Pashinyan for the second time since the start of the crisis and said all sides should take measures to de-escalate. It has not made public any contacts between Putin and Aliyev.
The Kremlin said Moscow was in constant contact with Turkey, Armenia and Azerbaijan. Any talk of providing military support for the opposing sides would only add fuel to the fire, it said.
US Democratic presidential candidate Joe Biden tweeted: "With casualties rapidly mounting in and around Nagorno-Karabakh, the Trump Administration needs to call the leaders of Armenia and Azerbaijan immediately to de-escalate the situation. It must also demand others - like Turkey - stay out of this conflict."
Pashinyan told the BBC in an interview that Azeri forces had shelled villages and towns in Nagorno-Karabakh and inside Armenia itself on Tuesday.
"There are casualties among both military and civilians. Dozens are killed and hundreds are wounded," he said.
Azerbaijan's prosecutor's office said 12 Azeri civilians had so far been killed and 35 wounded by Armenian fire. The Azeri side has not disclosed military casualties.
Nagorno-Karabakh has reported the loss of at least 84 soldiers.
"What can I say? It's a war. We hear air raids several times a day and hide in bomb shelters," Albert Voskanyan, a resident of the enclave's capital Stepanakert, told Reuters.
Armenian officials said earlier that a civilian was killed in an Azeri attack on the Armenian town of Vardenis, more than 20 km (12 miles) from Nagorno-Karabakh. They said a bus caught fire in the town after being hit by an Azeri drone.
Azerbaijan's defence ministry said that from Vardenis the Armenian army had shelled the Dashkesan region inside Azerbaijan. Armenia denied those reports.