Thousands of ethnic Armenians are without shelter in Nagorno-Karabakh's main city after fleeing Azerbaijan's military assault on the region.
Karabakh officials told the BBC that many families had been separated by Azerbaijani army positions and did not know if their relatives are alive.
There are also shortages of food and medicine.
However, the International Red Cross said it had managed to deliver 70 tonnes of relief aid on Saturday.
It was the first convoy to reach the disputed territory since Azerbaijan captured it in a lightning operation five days ago. A Red Cross spokesperson said a ceasefire appeared to be holding and more aid was expected. Russia says it has also delivered aid.
Nagorno-Karabakh is recognised internationally as part of Azerbaijan but large areas of it have been controlled by ethnic Armenians for three decades.
At least 200 ethnic Armenians died as Azerbaijan's army swept into the enclave. About 60 Azerbaijan troops are believed to have been killed during the assault.
Now, displaced from villages and separated from relatives, several thousand people were sleeping in tents or the open air near the airport in Stepanakert, known as Khankendi by Azerbaijan, Karabakh officials said.
The airport is also near a base for Russian peacekeepers, five of whom were killed during the fighting.
On Saturday Azerbaijan said it was working with Russian peacekeepers in Nagorno-Karabakh to disarm ethnic Armenian forces - one of its key demands in return for a ceasefire.
"The armed formations of Karabakh have begun handing over weapons and military equipment under the control of Russian peacekeepers," Russian officials said.
Russia's defence ministry said six armoured vehicles, more than 800 guns and about 5,000 units of ammunition had been handed over so far.
It is unclear what will happen to the 120,000 ethnic Armenians in Nagorno-Karabakh. Azerbaijan says it wants to reintegrate the region and an Azerbaijani official told the BBC that "no one is kicking anyone our anywhere".
"If we didn't care about civilians, women and children, we would have simply entered Khankendi," he said.
Azerbaijan has also said it envisages an amnesty for those Karabakh fighters who hand over their weapons and they can leave for Armenia if they choose.
Armenia has set up facilities to take in thousands of ethnic Armenians but Prime Minister Nikol Pashinyan has said he does not want them to leave Nagorno-Karabakh unless they have to.
However people in Stepanakert have told the BBC that many people are likely to choose to leave.
"I don't know anyone who wants to stay here. I have very close elderly relatives who lost their sons in previous wars and they prefer to die here," journalist Siranush Sargsyan said.
"But for most people, for my generation, it's already their fourth war."
US Senator Gary Peters, who is leading a congressional delegation to the Armenia-Azerbaijan border, said people in Nagorno-Karabakh were "very fearful" and called for an international observer mission there.
"I think the world needs to know exactly what's happening in there," he told reporters.
"We've heard from the Azerbaijani government that there's nothing to see, nothing to worry about, but if that's the case then we should allow international observers in to see."