The office of Nagorno-Karabakh's human rights ombudsman said more than a dozen shells had fallen on Stepanakert, the enclave's largest city, a day after a maternity hospital there was struck. Two civilians were wounded.
Azerbaijan's defence ministry said in a statement that Armenia had fired at its military units and civilian settlements along the front line, and that the Azeri settlements of Terter and Gornaboy to the north of Nagorno-Karabakh had been shelled.
The worst fighting in the South Caucasus for nearly 30 years has raised fears of a wider war that could suck in Russia and Turkey, an ally of Azerbaijan. It also poses a threat to pipelines carrying oil and gas from Azerbaijan to world markets.
Three ceasefires have failed to hold and civilians were killed on either side of the conflict on Wednesday.
"The European Union finds it unacceptable that after three agreements brokered by Russia, France and the United States on a ceasefire, the fighting in and around Nagorno-Karabakh still continues," European Commission foreign affairs and security policy spokesman Peter Stano said in a statement late on Wednesday.
The EU executive urged the sides to return without delay to "substantive negotiations" on a peaceful settlement as last agreed in Washington on Oct. 25.
The OSCE Minsk Group, formed to mediate the conflict and led by France, Russia and the United States, had been due to meet the Azeri and Armenian foreign ministers in Geneva on Thursday. It was not immediately clear whether this meeting would take place.
Turkey has demanded a bigger role in any peace negotiations.
The defence ministry of the Nagorno-Karabakh region said on Thursday it had suffered 51 more casualties, taking its military death toll to 1,119 since fighting erupted on Sept. 27.
Azerbaijan has not disclosed its military casualties. Russia has estimated as many as 5,000 deaths on both sides.
Nagorno-Karabakh is internationally recognised as part of Azerbaijan but is populated and controlled by ethnic Armenians. About 30,000 people were killed in a 1991-94 war in the region.
