Some 88,780 people have crossed into Armenia from Nagorno-Karabakh, according to Armenian government figures, quoted by the RIA news agency.
The exodus of ethnic Armenians from the breakaway region began after the fall of its separatist government last week following a military operation by Azerbaijan.
The enclave is to become a full part of Azerbaijan by the end of the year.
The Ambassador of Azerbaijan to Ireland said that his country offered the ethnic Armenian people an option to remain, but "we cannot force them to stay".
Speaking on RTÉ's Morning Ireland, Elin Suleymanov claimed they are leaving because of "uncertainty which follows 30 years of occupation of Azerbaijan by Armenia".
He asked: "Why is the formally diverse region of Nagorno-Karabakh in Azerbaijan now 100% Armenian?
"That is because everybody else has been ethnically cleansed.
"One million people in Karabakh and surrounding regions were ethnically cleansed in the 1990s.
"Now we don't want to do what they've done to us and that's why everybody, including the president and everybody in Azerbaijan, is offering them to stay.
"We understand that there is uncertainty. We understand that there is a fear of safety …. Those are understandable concerns given they are part of a conflict for a long time".
Mr Suleymanov said the same standard should apply to Nagorno-Karabakh as it does in Ukraine, Georgia and Moldova.
He said that Azerbaijan has restored its integrity and constitutional law in accordance with international law.
Yesterday, Armenia's Ambassador to Ireland told the same programme that the "forced depopulation" of the indigenous Armenian people from Nagorno-Karabakh was "a tragic loss for the Armenian people and for civilisation".
Varuzhan Nersesyan said that Azerbaijan made a "fake promise" of reintegration but it is "nothing but a policy of ethnic cleansing" and "nobody wants to stay … under Azerbaijani rule".
Armenians were subjected to a nine-month blockade, he said, and the "mass exodus" from the region began once the corridor reopened.
"Most likely, we're going to see the departure of most – the predominant part – of the population.
"There might be some who will decide to stay, but basically this population has the right to stay on its own indigenous land."
It is unfortunate that the international community did not create "robust conditions" to prevent this from happening, Mr Nersesyan said.
Death toll from fuel depot blast in Karabakh rises to 170 – media
The death toll from an explosion and fire at a fuel depot in Nagorno-Karabakh has risen to 170, Armen press news agency has reported, citing local officials in the region.
The blast occurred as thousands of ethnic Armenians fled the area.
The authorities have not given any explanation of the cause of the blast.
Rescue work at the site continues.