Myanmar's navy refused on Sunday to let journalists approach a remote island where more than 700 migrants are said to be held following their rescue last week.

Reporters have been trying to access Thamee Hla Island at the mouth of the Irrawaddy since the authorities announced that 727 people, including 74 women and 45 children, had been found drifting in a boat off Myanmar's coast and had been taken there.

They are part of a recent exodus of persecuted Myanmar Rohingya Muslims and Bangladeshi economic migrants who have fled the region en masse in a crisis that regional nations have struggled to deal with.

Journalists who tried to take small boats out to Thamee Hla Island were being turned around by navy patrol vessels and were ordered to delete any footage on their memory cards, said an AFP reporter on the nearby island of Haigyi.

Those returning said they had been ordered to sign documents promising not to try to make the journey again.

The navy was unavailable for comment Sunday.

Migrant boats are a hugely sensitive topic in Myanmar. Its discovery of two vessels crammed with people in recent weeks has deepened a tug of war between neighbouring Bangladesh and the formerly army-ruled nation over who is responsible for migrants found in the Bay of Bengal.

Myanmar refuses to recognise its 1.3 million Rohingya living in the western state of Rakhine as citizens. Instead it refers to them as "Bengalis" and alleges they are illegal immigrants from across the border.

They face daily discrimination including controls on their movements, family size and access to jobs, forcing tens of thousands to flee overseas -- usually to Malaysia. That exodus increased dramatically after 2012 when scores were killed in communal bloodletting in Rakhine.

Myanmar has been keen to portray those leaving its shores as Bangladeshi economic migrants and rejects widespread criticism that its treatment of the Rohingya is one of the root causes of the current exodus.

On Saturday a local official from Haigyi Island said the migrants were all Bangladeshis and would be taken to an area near the Bangladesh border in Rakhine state in the coming days.

But Bangladesh has insisted it will not take back any migrants who trace their origin to Myanmar.

And because Myanmar authorities refuse to use the term Rohingya, it is difficult to ascertain where exactly the migrants come from.

No media or aid group has yet been able to meet the migrants held on Thamee Hla Island to verify where they say they originate from.

A lucrative people-smuggling trade has long thrived in the region, largely ignored or colluded at by the authorities. But a recent crackdown by Thai police in the country's deep south threw smuggling networks into chaos as gangmasters abandoned their victims on land and sea.

In recent weeks more than 3,500 migrants have turned up on Thai, Malaysian or Indonesian soil and an estimated 2,500 more are still stranded at sea.