"India and the European Union expressed deep concern at the recent spate of violence in the Rakhine state of Myanmar that has resulted in the outflow of a large number of people from the state, many of whom have sought shelter in neighbouring Bangladesh", the joint statement said.
Bangladesh authorities plan to expand a refugee camp at Kutupalong near the border town of Cox's Bazar to accommodate the Rohingya.
Over half a million Rohingya refugees have fled Myanmar since the latest outbreak of violence in their home province of Rakhine State in late August.
Thousands of Rohingya Muslims, a minority ethnic group who live in the Rakhine state of Myanmar were captured in a video, swimming across the water to escape persecution and traveling to Bangladesh Thursday.
It conveyed as much to New Delhi, which in fact led to modifications in India's stance including pressure on Myanmar to rein in the security forces, and humanitarian aid to Bangladesh.
Mofazzal Hossain Chowdhury Maya, minister for disaster management and relief, said all the Rohingya would eventually be moved from 23 camps along the border and other makeshift camps around Cox's Bazar to the new zone.
There was widespread scepticism over whether any will be able to return and it remains unclear where the Rohingya would go if they did, since many of their villages have been burnt to the ground.
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"India remains deeply concerned at the situation in Rakhine state of Myanmar".
"This flow out of Myanmar has not stopped yet, it's into the hundreds of thousands of Rohingya (who are) still in Myanmar, we want to be ready in case there is a further exodus", said the UN's under secretary-general for humanitarian affairs, Mark Lowcock, in a Friday press briefing in Geneva.
The multilateral treaty under the United Nations defines who a refugee is, and sets out the rights of individuals granted asylum and the responsibilities of nations that provide asylum.
An EU delegation also joined the UN's whistle-stop trip to Rakhine, which took in Maungdaw and Rathedaung areas, explaining in a statement "this was not an investigation mission and could not be in the circumstances".
The Myanmar government has claimed that the Rohingyas are Bengali immigrants from the Indian subcontinent and has denied them citizenship.
"We demanded a halt to the genocide of the Rohingya", Hefazat spokesman Azizul Hoque Islamabad told AFP.