Karabakh leader Arayik Harutyunyan warned that it would now consider "military facilities in Azerbaijan's big cities" as legitimate targets.
"I call on the residents of these cities to immediately leave," Harutyunyan said in a post on Facebook.
The International Committee of the Red Cross on Sunday condemned the reports of "indiscriminate shelling and other alleged unlawful attacks using explosive weaponry in cities, towns and other populated areas".
'Bombs falling in the yard'
Azerbaijan claims to have taken control of a string of settlements in recent days as well as a strategically important plateau.
On Sunday Aliyev said his forces had retaken the town of Jabrayil, part of an area outside Karabakh seized by the separatists in the 1990s as a buffer zone, hailing it as an important victory. Armenia denied the claim.
Authorities in both countries have reported more than 250 dead since the Nagorno-Karabakh conflict began, including 42 civilians.
Armenian separatist forces have reported more than 200 dead — including 51 on Saturday — while Azerbaijan has not released any figures on its military casualties.