No Rohingya refugees voluntarily chose to return to Myanmar from camps in Bangladesh on the first day of a planned repatriation programme.
Under a joint deal between the two countries, authorities had wanted to move some 2,000 Rohingya on Thursday.
But the UN and rights groups say no-one should be forced to return, as the situation in Myanmar is not safe.
More than 700,000 Rohingya Muslims and others have fled to Bangladesh over the past year.
They were escaping violence and a military operation in western Rakhine state.
The UN has said senior Myanmar officials should be investigated and tried for genocide over the operation, which the army says was targeting militants.
After the planned repatriations were halted on Thursday, amid protests in the camps, senior Myanmar officials said they had been ready to process returnees and blamed the Bangladeshi side.
'They're sending us to die'
The refugees are mostly living in basic conditions in sprawling camps near the Bangladeshi border town of Cox's Bazar.
Myanmar and Bangladesh have agreed they should gradually be returned to Myanmar and thousands of people have been approved for return by Myanmar.
This has led to panic among the refugees, many of whom experienced violence in Myanmar, or had family members killed and their homes burned.
The first group of refugees due to leave on Thursday had been told buses had been organised, a transit camp set up and there were stocks of rations for three days, the BBC's Yogita Limaye reported from one of the camps.
But hearing the announcement people erupted in protest, shouting "we don't want to go back", and holding up placards listing the things they wanted before they would agree to return. Some even broke down in tears, our correspondent reports.
"None feels safe to go back now. We cannot force them to go back against their will," Mohammad Abul Kalam, Bangladesh's repatriation commissioner, told AFP news agency.
Amid the heightened anxiety, there is an increased security presence in the camps.
"I'm scared about the repatriation," one 40-year-old man on the list to be sent back told the BBC. "Though they are trying to reassure us, I'm not convinced. I think they might kill us if we go there."
Like many others he has sent his family into hiding in the camps. He said the only condition under which they were prepared to return to Myanmar was if they were given citizenship.
"If we have to go back, that is our fate. But I feel they will be sending us there to die."
Another refugee told the BBC he fled with his wife and sons but that many relatives had been killed.
"They brutally tortured us," he said, breaking down in tears. "The military came to us, they killed our people, threw kids in the fire and also set fire to houses.
"I am very disturbed by this talk of going back. How can we go there?"
'The Rohingya's biggest fear'
Nick Beake, BBC Myanmar correspondent, Rakhine state
The biggest fear for the Rohingya is that they would be living among the Buddhist mobs accused of burning their villages and would be protected by the same army troops who are accused of committing genocidal acts against them.
It's true that the Rohingya people are detested by large parts of Burmese society and particularly in Rakhine state where the worst persecution has played out.
Ethnic Rakhine villagers told me on a recent trip they believed all Rohingya were illegal and dangerous immigrants. The village administrator quietly said they were all "terrorists". These views - extreme and unswerving - are widespread in Rakhine state.
So while the Myanmar government talks about building temporary shelters, offering medical care and sufficient food rations for Rohingyas who return, many international observers insist the root causes of the violence and hate-filled attitudes need to be properly tackled before Rohingyas can return home and live with safety and dignity.
The UN, charities and human rights groups are concerned there is no effective plan in place to independently monitor the Rohingyas safety if they return.
"We are witnessing terror and panic among those Rohingya refugees in Cox's Bazar who are at imminent risk of being returned to Myanmar against their will," Michelle Bachelet, the UN High Commissioner for Human Rights said.
She warned that lives would be put at "serious risk" if the repatriation was to go ahead.
"The Bangladesh government will be stunned to see how quickly international opinion turns against it if it starts sending unwilling Rohingya refugees back into harm's way in Myanmar," Bill Frelick, refugee rights director at Human Rights Watch, said.
Why are the Rohingya in Bangladesh?
The Muslim Rohingya are one of the many ethnic minorities in Myanmar. Authorities in predominantly Buddhist Myanmar see them as illegal immigrants, so they are denied citizenship and other rights.
There have been widespread allegations of human rights abuses, including arbitrary killing, rape and burning of land over many years.
Last year, the Myanmar military launched a crackdown in Rakhine state after Rohingya militants carried out deadly attacks on police posts, sparking an exodus.
About 300,000 Rohingya had already fled Myanmar (also called Burma) in earlier waves of communal violence.
Myanmar's army has previously cleared itself of wrongdoing and has rejected UN allegations that genocide may have occurred.
The country's de-facto civilian leader Aung San Suu Kyi is currently in Singapore for an international summit where she was confronted by US Vice President Mike Pence over the issue.
"The violence and persecution by military and vigilantes that resulted in driving 700,000 Rohingya to Bangladesh is without excuse," he said.
She responded that there were "different points of view" and both sides should "learn to understand each other better".