"At least 14 people are dead while 11 remain missing in Badulla," police said.
Helicopters were deployed after flash floods caused mudslides and several roads were rendered impassable due to incessant rains.
The worst affected was Rilpola town in the central hill district of Badulla where five people were killed as mounds of earth fell on homes.
President Mahinda Rajapaksa has formed a relief committee for victims manned by commanders of government forces.
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Sri Lanka Railways said all train services from capital Colombo to the central hill areas of Kandy, Badulla and Matale were cancelled due to the severe weather conditions.
The Meteorological Department said that low pressure has increased into a depression located just off the southeast coast.
Strong winds up to 60 kph are expected and people have been asked to stay away from coastal areas.