According to TV channel NTV, at least 30 boats carrying Rohingya refugees have floundered in the river, which divides Bangladesh from the western Myanmar state of Rakhine, since August 25, resulting in around 200 deaths.
United Nations refugee agency (UNHCR) spokesman Andrej Mahecic expressed deep concern over the "condition of thousands of new arrivals who are stranded near the Bangladesh-Myanmar border".
Subramaniam said Malaysia is ready to provide medical personnel and aid in Cox's Bazar where numerous refugees fled to, but is now awaiting approval from the Bangladesh government.
"Every minute counts given the fragile condition they're arriving in", said Mahecic.
Many of the Rohingyas who arrived since Sunday told the UNHCR they were forced to leave when their villages were set on fire.
Numerous new arrivals were from Rakhine's Buthidaung district, which lies relatively far from the border with Bangladesh. "We walked all the way to this land to save our lives", said Mohammad Shoeb, who arrived at the border with his family on Monday evening.
"Twenty-one passengers were rescued, while many others are believed to have gone missing, " the officer said.
That figure does not include the thousands now in no man's land.
Almost 200 people have died in around a dozen boats sinking since the Rohingya influx began in late August after attacks by Muslim militants triggered what the Myanmar military has labelled "clearance operations".
These refugees were waiting to be registered by the Bangladeshi authorities before being transferred to camps raised to house them, Efe news reported.
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