The visit marks the first time in about three decades that the international body has gained access to the region.
An Azerbaijani presidency spokesman said the UN mission arrived in the region on Sunday morning, mainly to assess humanitarian needs.
The mission, led by a senior UN aid official, is the global body’s first access to the region in about 30 years.
Armenia has asked the International Court of Justice (ICJ) to order Azerbaijan to withdraw all its troops from civilian establishments in Nagorno-Karabakh and give the UN access.
The ICJ in February ordered Azerbaijan to ensure free movement through an area known as the Lachin Corridor leading to and from the region.
The World Health Organization on Sunday said well over 100,000 ethnic Armenians from Nagorno-Karabakh had travelled to neighbouring Armenia.
Armenian separatists, who had controlled the region for three decades, agreed to disarm, dissolve their government and reintegrate with Baku following a one-day Azerbaijani offensive last week.
‘Ghost town with no soul’
The end of Karabakh’s separatist bid dealt a heavy blow to a centuries-old dream by Armenians of reuniting what they say are their ancestral lands, divided among regional powers since the Middle Ages.
Nearly all of Karabakh’s estimated 120,000 residents fled the territory over the following days, sparking a refugee crisis.
Reporting from the Nagorno-Karabakh city that is called Stepanakert by Armenians and Khankendi by Azerbaijanis, Al Jazeera’s Osama Bin Javaid said tens of thousands of people deserted the area in the past few days in what can only be described as a “mass exodus”.
“Here in the town centre, if I go quiet, you will be able to hear nothing,” he said. “There is absolutely no one who is left here apart from some disabled and elderly.”
“A ghost town with no soul,” said Javaid, describing all that has been left behind.
The Azerbaijani presidency said Baku’s migration service has begun operating in the city to register Armenian residents to ensure their “sustainable reintegration … into the Azerbaijani society,” promising them the “patronage of the Azerbaijani state”.
Nazeli Baghdasaryan, a spokeswoman for the Armenian prime minister, said “100,490 forcefully displaced persons arrived in Armenia” by Sunday morning.
Yerevan has accused Baku of “ethnic cleansing” – an allegation Baku has rejected.
Armenia, a country of 2.8 million, faces a major challenge housing the sudden influx of refugees.
The International Federation of Red Cross and Red Crescent Societies on Friday announced an emergency appeal for 20 million Swiss francs ($22m) to help those fleeing.
Meanwhile, Azerbaijan is holding “reintegration” talks with separatist leaders while also detaining senior figures from its former government and military command.
Azerbaijan’s Prosecutor General Kamran Aliyev said criminal investigations had been initiated into war crimes committed by 300 separatist officials.
“I urge on those persons to surrender voluntarily,” he told journalists on Sunday.
Azerbaijan’s President Ilham Aliyev and Armenia’s Prime Minister Nikol Pashinyan are set to meet on Thursday in the Spanish city of Granada for Western-mediated talks aimed at ending their historic enmity.
With the two countries’ relations poisoned by ethnic hatred ensuing from three wars in as many decades, several rounds of negotiations mediated by Brussels and Washington have so far failed to bring about a breakthrough.