The death toll from the floods in Bangladesh has increased to 13 with injuries reported and millions stranded along the nation's southeastern coast following the region's annual monsoon rain, the disaster management ministry said in a bulletin.

This includes the main port of Chittagong and Cox's Bazar, a district housing approximately one million Rohingya refugees from Myanmar.

"It's a catastrophic situation here," rescue volunteer Zahed Hossain Bhuiya, 35, from the worst-hit city of Feni, told AFP. "We are trying to rescue as many people as we can."

The disaster management ministry stated that nearly 190,000 people were taken to emergency relief shelters while 4.5 million people were impacted in some way by the floods.

All major tributaries of the Himalayan rivers were overflowing, local media reported.

"Everything is underwater," 60-year-old Nur Islam said, whose house had been submerged by the flood.

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Areas east of the capital city of Dhaka have also been significantly affected by the floods, including the city of Comilla bordering India's Tripura state.

11 of the nation's 64 districts have been affected by the flood, the ministry reported.

Bangladesh accuses India of 'creating the flood' and its political turmoil

The majority of Banglesh's geography is made up of deltas where the Himalayan rivers, the Ganges and the Brahmaputra, flow towards the sea after passing through India.

The Indian Foreign Ministry rejected accusations made by some in Bangladesh that it was responsible for the floods, denying it had intentionally released water from an upstream dam. 

The Ministry attributed this phenomenon to the catchment area experiencing the "heaviest rains of this year over the last few days", and that the downstream flow was due to "automatic releases."

Asif Mahmud, the key organizer of the recent student-led anti-quota protests and newly appointed sports minister in the interim cabinet, accused India of not only supporting and sheltering former Prime Minister Sheikh Hasina but of deliberately "creating a flood."

"Floods on the common rivers between India and Bangladesh are a shared problem inflicting sufferings to people on both sides, and requires close mutual cooperation towards resolving them," New Delhi's foreign ministry said in a statement denying Mahmud's accusations.

The floods come after two months of political unrest in the country with violent protests and nationwide police crackdowns imposed by Hasina in response to anti-quota protests.