“He just slipped from my hands,” said Rashida, as she described the moment her seven-month-old son drowned, one of more than 60 people presumed dead when a boat carrying Rohingya Muslims capsized off the coast of Bangladesh.

As the vessel broke in two, and one piece sunk, the force of the water dragged her baby under.

Rashida’s mother and eight-year-old sister also died, but her father and two other sisters were rescued. The 23-year-old clutched a surviving sister’s hand as she recounted the accident from a hospital bed in Cox’s Bazar in Bangladesh, her knuckle white with tension.

Survivors of the accident said the boat was carrying about 80 people, including 50 children, when it overturned late on Thursday in rough waters just metres from the shore. Those onboard were escaping weeks of bloodshed in Myanmar’s Rakhine state, and seeking the safety of neighbouring Bangladesh. Many had travelled for days through thick forests before boarding the boat.

Twenty-three people have been confirmed dead and 40 are missing and presumed drowned, a spokesman for the International Organisation for Migration (IOM) told reporters in Geneva.

At another hospital, Mohamed Khasim mourned the loss of his wife and two of his daughters. His son clutched his father’s leg as another daughter stared blankly, frozen in shock.

“The water was choppy and there was this big wave, and the boat just fell apart,” Khasim said.

The boat had departed at 8pm on Wednesday evening for a journey that should have taken a couple of hours at most. But the crew appears to have got lost, and survivors described being out at sea all night, with no food.

“We begged the boatman to take us back, take us anywhere, just to get us off the boat,” Rashida said. When those on board finally saw land almost 24 hours later, they had no remaining food, little drinking water and dwindling fuel supplies.

On Friday, bodies, including children and babies, continued to float to the shoreline. “They drowned before our eyes. Minutes later, the waves washed the bodies to the beach,” said Mohammad Sohel, a shopkeeper.

More than half a million minority Rohingya Muslims have fled an army campaign that has been described by the UN human rights chief as a “textbook example” of ethnic cleansing.

The violence – the latest and most deadly upsurge in years of government oppression and communal hatred between Rohingya and Buddhists in Rakhine – exploded on 25 August when Rohingya insurgents attacked army posts.

A ferocious counter-offensive has destroyed more than 200 Muslim villages, which have been shown by satellite imagery to have been burned. Refugees in Bangladesh have recounted horrific stories of rape, mass murder and infanticide.

Speaking at a damning open session of the UN security council on Thursday night, the UN secretary general, António Guterres, said the conflict had become “the world’s fastest developing refugee emergency and a humanitarian and human rights nightmare”.

The US ambassador to the UN, Nikki Haley, lambasted the government of Aung San Suu Kyi for the bloodshed. “We cannot be afraid to call the actions of the Burmese authorities what they appear to be: a brutal, sustained campaign to cleanse the country of an ethnic minority,” she said. “And it should shame senior Burmese leaders who have sacrificed so much for an open, democratic Burma.”

Myanmar’s national security adviser, U Thaung Tun, denied the accusations. “I can assure you that the leaders of Myanmar, who have been struggling so long for freedom and human rights, will never espouse a policy of genocide or ethnic cleansing and that the government will do everything to prevent it,” he said.

He repeated a government line that 50% of Muslim villages in the north of Rakhine state, the heart of the violence, remain intact.

U Thaung Tun said Myanmar was “concerned by reports that thousands of people have crossed into Bangladesh” but said the country needed to “fathom the real reasons for the exodus”, which he blamed on “terrorists”.

Masud Bin Momen, Bangladesh’s representative to the UN, said it was evident why people were escaping. “Any individual among the new arrivals would make it known why this exodus is continuing. They all narrate use of rape as a weapon to scare families to leave,” he said.

Myanmar has blocked aid access to the region for UN humanitarian agencies, preventing civilians in the conflict zone from receiving food, water and medicine.

The UN in Myanmar says it is worried that many people are still on the move or trapped in remote areas far from the border and are unable to reach safety.

Meanwhile, aid workers in Bangladesh warn of a humanitarian catastrophe for hundreds of thousands of refugees kept in muddy camps over the border.

The BBC reported on Friday that the head of the UN in Myanmar had been accused of mishandling the longstanding issue by prioritising development in impoverished Rakhine over pushing for Rohingya rights.

It cited Caroline Vandenabeele, former head of office for the UN resident coordinator, Renata Lok-Dessallien, who said raising the Rohingya problem had negative consequences for UN staff. “An atmosphere was created that talking about these issues was simply not on,” she was quoted as saying.

The UN in Myanmar said it strongly disagreed “with the accusations that the resident coordinator ‘prevented’ internal discussions”.

Reuters and Agence France-Presse contributed to this report