Tens of thousands of refugees have fled Burma's province of Rakhine by boat. About 30,000 are already in camps in Bangladesh.
As many as 1,500 are said to have been turned back in recent days.
The UN's refugee agency in Geneva, the UNHCR, says women and children have been left adrift on boats in the river Naf without food or care.
"There are now a number of boats drifting in the mouth of the Naf River with desperate people onboard in need of water, food and medical care," the UNHCR said in a statement.
"It is vital that these people are allowed access to a safe haven and shelter."
The violence flared after the murder of a Buddhist woman last month, followed by an attack on a bus carrying Muslims which killed 10 people.
Burmese officials have said the fighting has killed 29 people and thousands of homes have been burnt down.