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Flash floods wrought havoc in Bangladesh on Friday as the country recovers from weeks of political upheaval, with the death toll rising to 15 and millions more caught in the deluge.

The South Asian nation of 170 million people, crisscrossed by hundreds of rivers, has seen frequent floods in recent decades.

Monsoon rains cause widespread destruction every year, but climate change is shifting weather patterns and increasing the number of extreme weather events.

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

Nur Islam, a shopkeeper in Feni, said his home had been completely submerged.

"Everything is underwater," the 60-year-old said.

Much of Bangladesh is made up of deltas where Himalayan rivers, the Ganges and the Brahmaputra, wind towards the sea after coursing through India.

All major tributaries of the two transnational rivers were overflowing, according to local media reports.

In India's hard-hit Tripura state, more than 23 people have died in the floods since Monday.

Bangladesh's disaster management ministry said in a bulletin that its latest toll of 15 deaths included fatalities in cities along the country's southeastern coast.

That included the main port city of Chittagong and Cox's Bazar, the latter a district home to around a million Rohingya refugees from neighbouring Myanmar.

Areas east of the capital Dhaka were also badly hit including the city of Comilla, near the border with Tripura state in India.

Nearly 190,000 others were taken to emergency relief shelters, according to the bulletin, while altogether 4.5 million people had been affected in some way.

Diplomatic tensions

The floods come less than three weeks after the ouster of ex-premier Sheikh Hasina, who was forced to flee by helicopter to India, her government's biggest political patron, during a student-led uprising.

Hasina's 15-year rule saw widespread human rights abuses, including the mass detention and extrajudicial killings of her political opponents.

She was replaced by Nobel laureate Muhammad Yunus, who is heading an interim government facing the monumental task of charting democratic reforms ahead of expected new elections.

Asif Mahmud, a leader of the student protests that ousted Hasina, and who is now in Yunus' caretaker cabinet, on Wednesday accused India of "creating a flood" by deliberately releasing water from dams.

India's foreign ministry rejected the charge, saying its own catchment area had experienced the "heaviest rains of this year" this week, and that the flow of water downstream was due to "automatic releases".

Hundreds of people nonetheless gathered at Dhaka University on Friday to protest India's "water aggression", featuring a banner showing Indian Prime Minister Narendra Modi delighting at the sight of drowning people.

"Water that has come from India has washed away all our euphoria," activist and poet Saikat Amin told AFP on the sidelines.

Relentless downpours have yet to abate on the Indian side of the border, with worst-hit Bagafa village recording 494 millimetres (19.4 inches) of rain in the 24 hours to Thursday.

State disaster agency official Sarat Kumad Das said most of the 23 people who have died in Tripura state were killed in landslides while a few drowned in flood waters.

Tripura chief minister Manik Saha said the situation was "still concerning" with relief efforts ongoing in the worst-hit parts of the state.

"Food is being distributed there, and we are also exploring the possibility of airlifting supplies," he said in a statement. "We are praying for everyone's safety."

Modi's Hindu-nationalist government backed Hasina's rule over her rivals from the Bangladesh Nationalist Party, which it saw as closer to conservative Islamist groups.

Modi has offered his support to the Yunus administration.