The group had boarded the vessel from internal displacement camps outside Sittwe, the capital of Rakhine state, Kyaw Htay said.
He added: “The boat was stopped after the engine failed.”
Fears have now been raised of a fresh wave of dangerous voyages being undertaken by those fleeing the country, similar to those seen after a crackdown on people smugglers in 2015.
More than 700,000 Rohingya refugees have fled to Bangladesh from western Rakhine state to escape brutal killings, gang rapes and the burning of their villages by the military and Buddhist vigilantes.
A UN-mandated investigation has accused the Myanmar army of genocide and ethnic cleansing.
Myanmar has denied almost all of the allegations, arguing security forces were battling terrorists and responding to attacks by Rohingya insurgents.
Officials earlier said they were ready to accept Rohingya who wanted to return from Bangladeshi refugee camps, but plans to repatriate several thousand fell through after the refugees protested, saying they did not want to return.
UN officials and aid agencies also opposed the plan, saying conditions in Myanmar were not safe.
There were 50 men, 31 women and 25 children among the refugees intercepted at sea, said Aye Mya Mya Myo, a politician for Aung San Suu Kyi’s ruling National League for Democracy party.
She posted pictures on Facebook of a rickety boat crammed with people. The boat resembled those typically used by Rohingya to escape the apartheid-like conditions in Rakhine, where they are denied free movement, education and healthcare.
For years, Rohingya on both sides of the border have boarded boats organised by smugglers in the dry months between November and March, when the sea is calm. But the perilous journey to Thailand and Malaysia, often undertaken in overcrowded vessels, has cost many lives.
Thailand cracked down on the trade after discovering a series of mass graves in 2015, leading to a crisis when smugglers abandoned their human cargo and left boats adrift in the Andaman Sea.
Additional reporting by Reuters
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies