That's after Azerbaijan military victory last week in a conflict that dates back to the fall of the Soviet Union.
"Armenians in Nagorno-Karabakh continue to face the threat of ethnic cleansing. In recent days, humanitarian aid has arrived in Nagorno-Karabakh, but this does not change the situation. And unless real living conditions are created for the Armenians of Nagorno-Karabakh in their homes and effective mechanisms of protection from ethnic cleansing, then the likelihood that the Armenians of Nagorno-Karabakh will see exile from their homeland as the only way to preserve their lives and identity increases significantly."
A mass exodus could change the delicate balance of power in the South Caucasus region, a patchwork of ethnicities crisscrossed with oil and gas pipelines where Russia, the United States, Turkey and Iran are jostling for influence.
On Sunday, a Reuters reporter saw heavily laden cars with civilians approach an aid center in the Armenian border village of Kornidzor.
Last week, Azerbaijan scored a victory over ethnic Armenians who have controlled the Karabakh region since the dissolution of the Soviet Union.
An adviser to the leader of the Karabakh Armenians told Reuters earlier on Sunday that the population would leave because they feel unsafe under Azerbaijani rule.
Russia had acted as guarantor for a peace deal that ended a 44-day war in Karabakh three years ago, and many Armenians blame Moscow for failing to protect the region.
Indeed, Pashinyan blamed Russia publicly on Sunday for failing to do enough for Armenia which he said would review its alliance with Moscow.
Russian officials say Pashinyan is to blame for his own mishandling of the crisis.
