Aliyev said in an address to the nation on Wednesday night that Baku's forces had "destroyed most" of the separatist forces and their military equipment and "reasserted their sovereignty" in the region, which has been disputed for decades with Armenia.
Aliyev on Wednesday offered residents of Karabakh ethnic Armenia and neighbouring Armenia prospects for cooperation, reconciliation and joint development after his forces seized control of the separatist enclave.
In a televised address, he said Azerbaijan had regained full sovereignty over its territory and now wanted to integrate the Karabakh population and turn the region into a "paradise".
He added that Azerbaijan has nothing against the Armenian people of Karabakh, who said "they are our citizens" but only against their "criminal" separatist leaders.
Azerbaijan appreciated the fact that Armenia, on whose support the Karabakh region had been dependent for three decades, had not sought to interfere in the Baku military operation, but had remained "watched". This improved the prospects for peace talks, he said.
Demonstrations in Yerevan
Thousands of Armenians demonstrated outside the residence of Armenian Prime Minister Nikol Pashinyan in Yerevan to protest the government's handling of the crisis in the Nagorno-Karabakh region, which is disputed with Azerbaijan.
Protesters, who blocked streets around the headquarters, accused the government of abandoning Armenians, who make up the majority of the region's population, after the military operation launched by Azerbaijan on Tuesday and ended about 24 hours later with the surrender of the separatists.
"We are losing our homeland and our people," Sarkis Hayats, a 20-year-old music worker, told AFP, adding that Pashinyan "must go, he is unable to rule the country".
After coming to power, Pashinyan vowed to change, but the humiliating military defeat to Azerbaijan in 2020 and the escalation in Nagorno-Karabakh tarnished his reputation.
The opposition has consistently accused Pashinyan of making major concessions over Karabakh.
"Everyone left Artsakh, my homeland has become helpless," Hasmik Manoukian, 47, said in tears, using Armenia's name for Karabakh.
He added that his country's authorities "believe that Artsakh is an unnecessary burden on Armenia, but it is not."
Soren Gavolyan, 26, said: "We will stay here and organize demonstrations," noting that "if Armenians unite, the enemy will not win."
Russia: Karabakh crisis is an Azerbaijani affair
In Moscow, the Russian presidency considered the Nagorny Karabakh crisis an "internal affair" of Azerbaijan.
Kremlin spokesman Dmitry Peskov said, "There is no doubt that Karabakh is an internal affair of Azerbaijan," stressing that the latter "disposes of territory belonging to it, which Armenian officials acknowledge," in remarks quoted by the agency "Interfax".