Yerevan said Nagorno-Karabakh's main city Stepanakert, which has been under artillery fire since Friday, was hit again on Sunday, AFP reported.
Azerbaijan's Defense Ministry said Ganja, a city of more than 330,000 in western Azerbaijan, was also "under fire" while separatist forces claimed to have destroyed an airbase there.
The two sides accused each other of targeting civilian areas, as the conflict appeared to be widening a week after heavy fighting broke out in the decades-old dispute over Karabakh.
Armenia and Azerbaijan have resisted international calls for a cease-fire and clashes have intensified in recent days, with both sides claiming victories on the front and saying they are inflicting heavy losses.
Sirens were sounding and explosions were heard at regular intervals in Stepanakert, where residents were taking shelter including several families in the basement of a church.
Armenia's Foreign Ministry said Stepanakert and the town of Martakert were under rocket attack and accused Azerbaijani forces of "the deliberate targeting of the civilian population."
It said the air force was also involved. Drones could be heard flying over Stepanakert.
Azerbaijan said Ganja was under fire, including from areas outside of Karabakh.
"Armenian forces struck Ganja with rockets from Armenian territory," said Hikmet Hajiyev, an advisor to Azerbaijani President Ilham Aliyev.
He said Armenian forces had also used heavy artillery and rockets against the towns of Terter and Goradiz in Azerbaijan.
Karabakh's separatist forces said they had targeted and destroyed an airbase in Ganja, while the region's leader, Arayik Harutyunyan, warned that it would now consider "military facilities in Azerbaijan's big cities" as legitimate targets.
Azerbaijan claims to have made gains in Karabakh in recent days, with its Defense Ministry saying that 14 settlements have been taken as well as a strategically important plateau.