Thousands more refugees fled Nagorno-Karabakh on Tuesday as officials in the self-proclaimed republic said a fuel depot explosion the previous day had killed 20 people.
The Armenian government has warned of possible "ethnic cleansing" by Azerbaijan following its lightning offensive against the breakaway region last week.
Armenia said on Tuesday that more than 13,000 refugees had fled since a first group arrived in the country on Sunday.
The influx overwhelmed the border town of Goris, where many refugees are staying.
Many slept in their cars laden with luggage, emerging on Tuesday with red-rimmed eyes and forming long queues outside phone shops to buy sim cards.
Azerbaijan has pledged equal treatment for residents of the majority ethnic Armenian enclave and has sent aid.
Adding to humanitarian concerns, the separatist government on Tuesday said 13 bodies were found at the scene of a fuel depot blast on Monday and seven more people had died of their injuries.
It said in a statement that 290 people had been hospitalised and "dozens of patients remain in critical condition".
Armenia's health ministry said it had sent a team of doctors to the rebel stronghold of Stepanakert by helicopter.
The Azerbaijani presidency said Baku had also sent medicine to help the wounded.
Meanwhile in Brussels, envoys from Baku and Yerevan prepared to meet in the first such encounter since Azerbaijan's swift defeat of separatist forces last week.
Simon Mordue, chief diplomatic adviser to European Council president Charles Michel, will chair the talks, Michel's spokeswoman said.
Azerbaijan and Armenia, along with EU heavyweights France and Germany, will be represented by their national security advisers.
The leaders of both countries are scheduled to meet next month.
AFP reporters on Monday saw the refugees crowding into a humanitarian hub set up in a local theatre in the city of Goris to register for transport and housing.
"We lived through terrible days," said Anabel Ghulasyan, 41, from the village of Rev, known as Shalva in Azeri.
She arrived in Goris with her family by minibus, carrying her belongings in bags.
- Years of conflict -
Armenia and Azerbaijan have fought two wars in the last three decades over Nagorno-Karabakh, a majority ethnic Armenian enclave within the internationally recognised border of Azerbaijan.
Azerbaijan's operation on September 19 to seize control of the territory forced the separatists to lay down their arms under the terms of a ceasefire agreed the following day.
It followed a nine-month blockade of the region by Baku that caused shortages of key supplies.
The separatists have said 200 people were killed in last week's fighting.
Azerbaijan's state media on Monday said officials held a second round of peace talks with Nagorno-Karabakh's ethnic Armenian community aimed at "reintegrating" them.
But on the road heading to Armenia, more and more residents from the region appeared to be trying to get out as witnesses said cars were snarling up in traffic.
At the refugee centre in Goris, Valentina Asryan, a 54-year-old from the village of Vank who fled with her grandchildren, said her brother-in-law was killed and several other people were injured by Azerbaijani fire.
"Who would have thought that the 'Turks' would come to this historic Armenian village? It's incredible," she said, referring to the Azerbaijani forces.
She was being housed temporarily in a hotel in Goris and said she had "nowhere to go".
Source: BSS/AFP