The flood situation in Sylhet and Sunamganj districts has worsened further due to constant heavy rain and onrush of water from the hills.
According to BSS, at least 4.0 million people were marooned and 300,000 people were facing electricity outages in those districts, officials said.
All the Upazilas and half of Sylhet city, all Upazilas and municipalities of Sunamganj district, the Sylhet-Sunamganj highway and the Sylhet-Bholaganj Bangabandhu Sheikh Mujibur Rahman highway are already submerged.
The Meteorological Department has forecast heavy to very heavy rain in the next 48 hours.
The power supply system has been cut off at Kumargaon station, one of the power substations of Sylhet, at around 12pm on Saturday.
Reuters said in a report that lightning strikes have killed at least 15 people in eight districts in Bangladesh since Friday, and four people were killed in landslides.
The flooding in Bangladesh, described by a government expert as potentially the country's worst since 2004, was exacerbated by the runoff from heavy rain across Indian mountains. The rain continued on Saturday, with more forecast over the next two days.
"Much of the country's northeast is underwater and the situation is getting worse as heavy downpour continues," said Mohammad Mosharraf Hossain, chief administrator of Bangladesh's Sylhet region.
Seasonal monsoon rains, a lifeline for farmers across South Asia, also typically cause loss of life and property every year.
Bangladesh has experienced increasing extreme weather in recent years, causing large-scale damage. Environmentalists warn climate change could lead to more disasters, especially in low-lying and densely populated Bangladesh.
The worst-hit Sunamganj district is almost disconnected from the rest of the country, Mosharraf Hossain said, adding that authorities helped by the army were focused on rescuing those trapped and distributing relief.
"There is a shortage of boats, which makes it harder to move people to safer places," he said. "Today the navy is joining us in rescue efforts."
Television footage showed Bangladesh roads and railway lines submerged, with people wading through chest-high brown churning waters, carrying their belongings and livestock.
Many of Bangladesh's rivers have risen to dangerous levels, said Arifuzzaman Bhuiyan, head of the state-run Flood Forecasting and Warning Centre.
Syed Rafiqul Haque, a former lawmaker and ruling party politician in Sunamganj district, said a humanitarian crisis could emerge if the floods did not recede and proper rescue operations were not conducted. "The situation is alarming," he said.
"There is no electricity, no road connection, no mobile network. People are desperately in need of immediate shelter and food."
