He said that Armenian forces "must leave our territories, not in words but in deeds", provide a timetable for a full withdrawal, and recognize the territorial integrity of Azerbaijan.
Yerevan rejected Aliyev's demands.
"Conditionality is not acceptable, (Aliyev) must renounce the use of force and engage constructively in negotiations without imposing maximalist positions," Armenian foreign ministry spokeswoman, Anna Nagdalyan, told AFP.
'Chase them like dogs'
Sirens were sounding and explosions could be heard at regular intervals in Stepanakert, as residents took shelter, including several families in the basement of the city's Holy Mother of God Cathedral.
Armenia's Foreign Ministry said Stepanakert and other towns had been hit, accusing Azerbaijani forces of "the deliberate targeting of the civilian population".
There were reports of dead and wounded civilians in Stepanakert and the historic town of Shusha.
Azerbaijan said Ganja was under shell fire, including from areas outside of Karabakh in Armenian territory, with at least one civilian killed.
Azerbaijan's ally Turkey accused Armenia of "targeting civilians" in Ganja and reiterated support for its fellow Turkic and Muslim country as "one nation, two states".