Azerbaijan and the ethnic Armenian enclave of Nagorno-Karabakh said there were attacks from both sides at several directions along the line of contact that divides them.
The fighting has spread well beyond the borders of the enclave, threatening to spill into all-out war between the former Soviet republics of Azerbaijan and Armenia.
Armenia's Prime Minister Nikol Pashinyan, who spoke by phone to Russian President Vladimir Putin on Tuesday, said he was not at this point considering asking for help under a post-Soviet security treaty but did not rule out doing so.
"Armenia will ensure its security, with the participation of the Collective Security Treaty Organisation (CSTO) or without it," Russian news agencies quoted Pashinyan as saying.
He said he and Putin had not discussed the possibility of Russian military intervention in the Nagorno-Karabakh conflict.
Russia has used the CSTO, along with the Eurasian Economic Union, another regional bloc focused on trade, to project influence across most of the former Soviet Union.
Nagorno-Karabakh is a breakaway region that is inside Azerbaijan but is run by ethnic Armenians and is supported by Armenia. It broke away from Azerbaijan in a war in the 1990s but is not recognized by any country as an independent republic.
Any move to all-out war could drag in Russia and Turkey, which is a close ally of Azerbaijan.
The Azeri prosecutor's office said on Wednesday seven more civilians were wounded as a result of shelling of the city of Terter, which borders Nagorno-Karabakh.
Its defense ministry said ethnic Armenian forces attempted to recover lost ground by launching counter-attacks in the direction of Madagiz, but Azeri forces repelled the attack.
Armenia's defense ministry said the Azeri army had been shelling the whole front line during the night and two Azeri drones were shot down in the town of Stepanakert, Nagorno-Karabakh's administrative center. It was not possible to independently confirm the report.Dozens of people have been reported killed and hundreds wounded since the new wave of fighting broke out on Sunday.