By By Kathryn Armstrong & Nataliya Zotova for BBC
Refugees load their cars as they leave the Red Cross registration center, in Goris, on September 25, 2023. Photo: AFP / Alain Jocard
More than 6,500 people have so far crossed into Armenia from the enclave, which is home to a majority of some 120,000 ethnic Armenians.
They left after the government in Yerevan announced plans to move those made homeless by the fighting.
It also warned that those who stayed could face ethnic cleansing.
Azerbaijan has said it wants to re-integrate the ethnic Armenians as "equal citizens".
The first group of Nagorno-Karabakh refugees since Azerbaijan's lighting assault against the separatist region entered Armenia . Photo: AFP / Alain Jocard
The BBC has spoken to some of the refugees who arrived in the city of Goris on Sunday, close to the border between Armenia and Karabakh.
"I gave my whole life to my homeland," said one man.
"It would be better if they killed me than this."
A woman, Veronica, told the BBC that this was the second time she had become a refugee. The first time was during the conflict in 2020.
The main square of Goris was crowded. The theatre nearby was turned into a base for the Red Cross.
Tatiana Oganesyan, doctor and head of a foundation of doctors and volunteers that is now helping refugees in Goris, told the BBC that people who come to the doctors are exhausted, malnourished and psychologically crushed.
"People are shocked, they are telling us: I need pills, they are blue," she said. Doctors then need to figure out their medication and find it for them.
"We have nothing," said an elderly woman who just arrived in Goris. She pointed at her jumper, saying it was all she could bring with her from home. Her son was on crutches near her.
In the nearby village of Kornidzor, refugees who were being processed said they did not believe they could be safe under Azerbaijani rule and did not expect ever to be able to return home.
The Armenian government said in a statement on Sunday that hundreds of the refugees had already been provided with government-funded housing.
But it has not released a clear plan of how it could cope with an influx of people. Prime Minister Nikol Pashinyan announced last week that plans were in place to look after up to 40,000 refugees.
Armenians the BBC has spoken to have said they are prepared to take refugees into their homes.
Meanwhile, more than 140 people have been arrested in Yerevan on Monday following the latest anti-government protests, according to local media quoting the country's interior ministry.
The Tass news agency said special forces had begun detaining demonstrators who blocked roads in Yerevan.
Police were also stationed outside the main government building, which houses the prime minister's offices and which demonstrators have been trying to break into.
Protests first broke out last week over the government's handling of the crisis in Nagorno-Karabakh.
Pashinyan has been accused of granting too many concessions to Azerbaijan and there are calls for his resignation.
The Armenian separatist forces in the territory agreed to disarm on Wednesday, following a lightning-fast Azerbaijani military offensive.
Armenia has repeatedly said a mass exodus from the region would be the fault of the Azerbaijani authorities.
In a TV address on Sunday, Pashinyan said many inside the enclave would "see expulsion from the homeland as the only way out" unless Azerbaijan provided "real living conditions" and "effective mechanisms of protection against ethnic cleansing".
He repeated that his government was prepared to "lovingly welcome our brothers and sisters".
But David Babayan, an adviser to Nagorno-Karabakh's ethnic Armenian leader Samvel Shahramanyan, told Reuters he expected almost everyone to leave.
His people "do not want to live as part of Azerbaijan - 99.9 percent prefer to leave our historic lands", he said.
"The fate of our poor people will go down in history as a disgrace and a shame for the Armenian people and for the whole civilised world," he told Reuters.
"Those responsible for our fate will one day have to answer before God for their sins."
Nagorno-Karabakh - a mountainous region in the South Caucasus - is recognised internationally as part of Azerbaijan, but has been controlled by ethnic Armenians for three decades.
The enclave has been supported by Armenia - but also by their ally, Russia, which has had hundreds of soldiers there for years.
Five Russian peacekeepers were killed - alongside at least 200 ethnic Armenians and dozens of Azerbaijani soldiers - as Azerbaijan's army swept in last week.
On Sunday, Azerbaijan's defence ministry said it had confiscated more military equipment including a large number of rockets, artillery shells, mines and ammunition.
Despite Azerbaijan's public reassurances, there are fears about the residents of Nagorno-Karabakh, with only one aid delivery of 70 tonnes of food having been allowed through since separatists accepted a ceasefire and agreed to disarm.
Ethnic Armenian leaders say thousands are without food or shelter and sleeping in basements, school buildings or outside.
- This story was first published by BBC