The refugees said they witnessed children drowning and starving to death during their perilous journey.
The shooting took place after Bangladesh border guards turned back six boats of refugees as they tried to enter the country from neighbouring Burma across the river Naf to Teknaf town in the southernmost part of mainland Bangladesh, the witnesses told RFA.
"We floated in the sea for four days and my younger brother starved to death," said Minara Begum, a 10-year-old girl, speaking through an interpreter.
"We had six boats. Then a helicopter came and opened fire, and three boats were lost, all of those people [in them] were killed," She did not specify the exact date of the incident, which occurred earlier this month, or whether the helicopters were from Burma or Bangladesh.
Minara Begum, who is from Sittwe, the capital of violence-hit Rakhine state in Burma, is among a group of refugees sheltered and hidden from the authorities by a Bangladeshi woman.
The woman said she was moved by the plight of the Rohingyas, a stateless people described by the U.N. as one of the world's most persecuted minorities.
Mohammed Islam, a young father also from Sittwe, said he was among those who left in the group of six boats, three of which he said came under helicopter fire.
"Because we couldn't endure the torture, we took six boats and left our homeland," he said, citing burning of homes and mosques and killings and other sectarian violence triggered in the first week of June in which he said two of his children and up to 25 of his relatives died.
"Three [boats] were together and three became separated from the group," he said. "These three that fell behind were set on fire by the helicopters."
"At first, we couldn’t be sure that the boats were being fired on because of the sound of our engine but then we saw the boats catch fire."
Mohammed Islam said three children died on his boat. "We threw them into the sea because they were dead."
Another 10-year-old girl, Nahida Begum, said she was the only child who managed to swim ashore after their boat was turned back. The vessel, carrying her grandmother and many other children, including a nursing infant, was very small, not seaworthy, and possibly took on water.
A woman, Shahra Khatun, said her boat was turned back twice and although it managed to land on its third attempt, three children on the vessel, including two of her's, died while waiting out at sea.
"My five-year-old boy died of starvation and heat on the boat," she said. "They burned all of our homes and killed my sisters and brothers. That's why I came here," she said referring to the violence in Rakhine state which has left about 60 dead with tens of thousands displaced, according to official estimates.
At least 2,000 Rohingyas have tried to enter Bangladesh following the violence between Muslims and Buddhists in Rakhine state in Burma since early June but most were either turned back or detained.
In a June 18 incident cited by witnesses who spoke to RFA, the Bangladesh authorities turned back about 130 mostly young Rohingya men.
"This is the first time I have ever done anything like this," said a Bangladesh security officer, identifying himself as Major Salif, who oversaw a feeding program for the 130 Rohingyas before they were put back on their boats and sent away.
"According to my understanding, this [turning back the refugees] will go on for sometime but God willing it will take its natural course and settle down soon," Salif, the commanding officer at the Shapuri Dip Jetty in Teknaf, told RFA.
Bangladesh says its resources are already too strained and has refused to accept the Rohingyas despite appeals from the United Nations to grant them refugee status.
Bangladeshi officials estimate that a total of 300,000 Rohingya people live in the country, with only about a tenth of them in two official refugee camps in the southern district of Cox's Bazaar.
Burma considers the Rohingya to be illegal immigrants from Bangladesh and denies them citizenship while Bangladesh says Rohingya have been living in Burma for centuries and should be recognized there as citizens.
Reported by an RFA correspondent in Bangladesh.