At least 125 people were killed and 300 injured in an explosion at a fuel depot in the disputed Nagorno-Karabakh region late on Monday, Interfax Azerbaijan reported on Tuesday, quoting the Armenian Health Ministry.
The bodies of those killed in the blast, near Stepanakert, capital of Nagorno-Karabakh, have been sent to Armenia, it said.
Many people are still unaccounted for.
Separatist authorities earlier said most of the injured were in a "severe or extremely severe" condition.
"The medical capacities [of Nagorno-Karabakh] are not enough," said the region's rights ombudsman Gegham Stepanyan. He called for air ambulances to be allowed to land in the region.
Armenia's Health Ministry said it sent a team of doctors to the separatist stronghold of Stepanakert by helicopter.
Azerbaijan's presidency said Baku had also sent medicine to help those injured in the blast.
Thousands of people have since fled the enclave amid fears of ethnic cleansing.
Envoys from Baku and Yerevan are set to hold talks in Brussels on Tuesday after Azerbaijan's takeover of the majority ethnic Armenian enclave.
Most of the victims were stocking up on fuel for the trip down the so-called Lachin corridor, connecting the impoverished and historically disputed region with Armenia.
Armenians, mostly Christian, and Azeris, mostly Muslim, have fought two wars over the mountainous territory since the Soviet Union's 1991 collapse, which have claimed tens of thousands of lives.
The area is now populated by up to 120,000 ethnic Armenians but is internationally recognised as part of Azerbaijan.
Envoys from Baku and Yerevan were in Brussels on Tuesday to pave the way for the first meeting between their leaders since last week's offensive.
Simon Mordue, chief diplomatic adviser to European Council President Charles Michel, will lead the talks, Mr Michel's spokeswoman said.
Azerbaijan and Armenia, along with EU heavyweights France and Germany, will be represented by their national security advisers.
A senior US aid official on Tuesday said the country would stand in solidarity with Armenia.
Samantha Power, head of the US Agency for International Development (USAid), said it was essential the international community gained access to Karabakh, amid reports of unknown numbers of people being injured and requiring evacuation, or lacking food and essentials.
She appealed to Azerbaijan to allow the delivery of desperately needed humanitarian aid to Armenian civilians in Karabakh, describing the situation there as "harrowing".
Meanwhile, Kremlin spokesman Dmitry Peskov said any international observer mission for the Nagorno-Karabakh region could take place only with the agreement of Azerbaijan.
'We lived through terrible days'
Armenia said on Tuesday afternoon more than 19,000 people had crossed into the country since Sunday.
The influx overwhelmed the border town of Goris, where many refugees are staying.
"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 on a minibus.
Valentina Asryan, 54, fled to Goris with her grandchildren and said her brother-in-law was killed by Azeri gunfire.
"Who would have thought that the 'Turks' would come to this historic Armenian village? It's incredible," she said, referring to Azeri forces.
Many slept in their cars laden with luggage and on Tuesday formed long queues outside phone shops as they waited to buy Sim cards.
The stream of refugees continued on Tuesday, with hundreds of vehicles heading to Armenia from Nagorno-Karabakh.
Families piled their belongings on top of their cars and stopped for only a few seconds at the last Azeri checkpoint before entering Armenia along the Lachin corridor.
Azerbaijani border agents were looking for "war crime" suspects among the flood of refugees leaving its separatist enclave for Armenia, according to a government source.
"Azerbaijan intends to apply an amnesty to Armenian fighters who laid down their arms in Karabakh. But those who committed war crimes during the Karabakh wars must be handed over to us," the source said, explaining why men of fighting age were told to look into a camera at the last border checkpoint.
Last week, an offensive by Baku's forces established Azeri control over the breakaway region, forcing ethnic Armenian fighters to disarm.
US Secretary of State Antony Blinken spoke with Azerbaijan's President Ilham Aliyev on Tuesday on a phone call, asking for his country to "refrain from further hostilities" in the region.
His spokesman Matthew Miller said Mr Blinken also called on Mr Aliyev to "provide assurances to the residents of Nagorno-Karabakh that they can live secure in their homes and their rights will be protected".
Mr Miller said Mr Blinken requested that an international observer mission be allowed in.
Turkish President Recep Tayyip Erdogan held talks with Mr Aliyev on Monday, saying Baku's military victory opened a "window of opportunity" to normalise relations.
On Tuesday, a day after he met Azerbaijan's leader, Mr Erdogan said the Zangezur trade corridor passing through Armenia, Azerbaijan and Iran must be completed.
Speaking to reporters on his return flight from the Azeri exclave of Nakhchivan, where he had met Mr Aliyev, Turkey's President said if Armenia did not allow the trade corridor to pass through its territory, then Iran was warm to the idea of allowing it.
The Zangezur corridor aims to give Baku unimpeded access to Nakhchivan through Armenia.
Turkey and Azerbaijan have been calling for the corridor to be introduced since the Second Karabakh War in 2020.
Azerbaijan's offensive began on September 19 and forced separatists to lay down their arms under the terms of a ceasefire agreed on 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.
Baku announced two of its soldiers also died when a mine exploded on Sunday.
Azerbaijan's state media reported that officials have held a second round of peace talks with Nagorno-Karabakh's ethnic Armenian community aimed at "reintegrating" them.