Coastguard says the boat had been at sea for about two months after failing to reach Malaysia.
Hundreds of Rohingya rescued by Bangladesh and sent to a flood-prone island after being stranded at sea for weeks should be moved to existing refugee camps, the UN secretary-general said.
Antonio Guterres made the appeal to Bangladesh’s foreign minister in a letter that was obtained on Sunday by AFP news agency.
The Rohingya were rescued in early May after floating adrift in the Bay of Bengal and sent to Bhashan Char island – a silty strip of land that is vulnerable to monsoon storms.
Dhaka has said the 308 were sent to the island rather than the camps in Cox’s Bazar because authorities were afraid they might have the viral disease, also known as COVID-19.
Guterres said the refugees should be moved to the camps after their time in quarantine is completed.
Dhaka has not said how long the Rohingya will remain in isolation.
“While those rescued at sea may be quarantined for public health purposes, they must also be extended the protection they deserve as refugees,” Guterres said in the letter to Foreign Minister AK Abdul Momen dated Friday.
“I trust that they too, will benefit from the humanitarian services offered to the Rohingya in Bangladesh and that, at the end of their quarantine period… they will be allowed to rejoin their families in Cox’s Bazar.”
Momen told AFP he had yet to receive the letter but said those concerned about Bhashan Char – where facilities for 100,000 people were built last year – should host the Rohingya in their own countries.
“We don’t want any more Rohingya,” Momen told AFP.
“We don’t have any other place to keep them. If they (other countries) don’t like Bhashan Char, let them take them back to their countries. (Or) else, let them return to Myanmar.”
The foreign minister previously said the refugees would “most likely” have to live in the shelters on Bhashan Char until they return to Rakhine.
Nearly one million Rohingya live in crowded camps in Cox’s Bazar. Many fled Myanmar after a 2017 military crackdown.
Emergency teams are racing to contain the spread of the coronavirus in the camps after the confirmation of four cases.
Meanwhile, Amnesty International reported on Friday that at least 1,000 Rohingya remain stranded off the coast of Indonesia’s Aceh as Southeast Asian nations tighten their borders.
The group urged immediate action to ensure they were not buried in an “invisible graveyard” at sea.
Saad Hammadi, from the South Asia Regional Office of Amnesty International, said the refugees could have been sailing for several weeks or even months without food or water, citing information from humanitarian agencies and local news reports.