Thousands of homes were damaged and the storm Rashmi brought down electrical and telephone poles and uprooted trees. Large areas of acres of crops were also destroyed, officials said.
The two people were killed when their homes collapsed in a village in the coastal Bhola district 350 km (219 miles) south of the capital Dhaka.
Offshore islands and coastal areas were swept by a tidal surge of up to two meters above normal, but details of casualties were yet to be available.
Officials said thousands of people had been evacuated to shelters after the authorities issued storm warnings but the storm appeared to be weakening.
"It has turned into a land depression and started weakening gradually," a senior official of the Bangladesh Meteorological Department said.
Storms batter the poor south Asian country every year. Cyclone Sidr ravaged the coast last November, killing nearly 3,500 people and displacing some two million.
(Reporting by Nizam Ahmed; Editing by Valerie Lee) (email@example.com; +880-2-8330123; Reuters Messaging: firstname.lastname@example.org))
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