The UN refugee agency, which had previously refused to provide humanitarian services on Bhasan Char until assessments were completed, did not respond to request for comment on why the deal, signed in early October, had not been made public or its contents.
In a 9 October statement, the agency said the agreement covered “key areas of protection, education, skills-training, livelihoods and health, which will help support the refugees to lead decent lives on the island and better prepare them for sustainable return to Myanmar in the future”.
Bangladeshi government spokespeople were not available for comment but one official, who declined to be identified because they were not authorised to speak to media, questioned the need for free movement.
"Why will we will offer them freedom of movement? We are providing everything they need. They will have to stay in the camps until they go back to Myanmar," the official told Reuters.
Bangladesh says another 81,000 refugees will be moved to the island in coming months.
A leaked copy of the deal seen by Reuters says the United Nations would be “permitted unhindered access” to the population and further relocations would be voluntary.
But it said any travel between the island and mainland would be on an “as needs” basis, the precise details of which would be determined between the United Nations and Bangladesh, though refugees can “move on and within Bhasan Char for their daily activities”.
The deal refers to Rohingya as "forcibly displaced Myanmar nationals/refugees", reflecting the refusal of Bangladesh, which is not a signatory to the 1951 Refugee Convention, to confer refugee status on the group.
In a statement on Friday, the non-profit organisation Fortify Rights, which said it had examined the agreement, called on the United Nations and Bangladesh to revise it to include freedom of movement to the mainland.
“UNHCR’s lifesaving services are essential and needed on the island, but the agency must ensure it is not propping up a refugee prison with this agreement,” said the group's regional director, Ismail Wolff.
A refugee on the island, who asked not to be identified for fear of retribution, told Reuters by telephone life on the island was hard.
"Those who are living here can't go to meet their relatives. That's one of the reasons some Rohingya try to flee," the refugee said.
"We don't have the right to liberty of movement. We are confined here but no one cares. Our fate is to be stuck," said another refugee, who also requested anonymity.
Refugees on the mainland are also not allowed to leave their camps along the border. Rights groups have been calling for an end to restrictions on movement.
More than a million Rohingya live in Bangladesh after fleeing Myanmar, the vast majority in 2017 after a military crackdown that included mass killings and gang rapes and which the United Nations said was carried out with genocidal intent.
Myanmar denies genocide, saying it was conducting a legitimate campaign against insurgents who attacked police posts.