Floods and landslides triggered by heavy rain have killed at least 40 people and injured 10 across Sri Lanka this week, with 21 others missing, authorities said.

Most of the deaths occurred in the central tea-growing district of Badulla, where 21 people were buried alive when mountain slopes crashed onto their homes overnight, the Disaster Management Centre (DMC) said in a statement on Thursday.

Another four were killed similarly in the adjoining Nuwara Eliya district. The remaining fatalities were reported elsewhere.

The DMC said river levels were rising across Sri Lanka and warned residents in low-lying areas to move to higher ground.

Sri Lanka is currently experiencing the northeast monsoon season, but rain has intensified due to a depression east of the island, it added.

The government suspended final year school examinations nationwide for two days because of the weather.

Sri Lanka's parliament suspended a budget debate so that legislators could return to their constituencies to deal with the damage.

More than 100 millimetres of rainfall was expected across Sri Lanka, with some areas in the northeast forecast to be deluged with 250 millimetres of rain on Thursday.

This week's weather-related toll is the highest since June last year, when 26 people were killed following heavy rains. In December, 17 people were killed by flooding and landslides.

The worst flooding this century was in June 2003, when 254 people were killed.

Sri Lanka depends on seasonal monsoon rain for irrigation and hydroelectricity, but experts have warned that the country faces more frequent floods due to climate crisis.