Thousands more fled Nagorno-Karabakh on Tuesday as separatists said a fuel depot explosion the previous day had killed 20 people.
Armenia said on Tuesday that more than 13,000 refugees had fled since the first group arrived in the country on Sunday. The influx overwhelmed the border town of Goris, where many refugees are staying.
Azerbaijan has pledged equal treatment for residents of the majority ethnic Armenian enclave and has sent aid.
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”.
Read: Azerbaijan says Armenia breaches Russian ceasefire after border clash
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.
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.
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.