Sri Lanka stopped passenger trains and closed roads in some parts of the country where landslides and floods triggered by heavy rains have caused more than 40 deaths, officials said on Thursday.

The government's disaster management centre said 25 of the reported deaths occurred in the mountainous tea-growing regions of Badulla and Nuwara Eliya in the country's central province about 300 kilometres east of the capital, Colombo.

Another 21 people were missing on Thursday due to landslides in the same areas, while 10 people were injured, the centre said.

Reservoirs and rivers have overflowed, blocking roads. Some key roads connecting the provinces have been closed, officials said.

Authorities stopped trains in some areas in the mountainous region after rocks, muds and trees fell onto railway tracks, and local television showed workers removing the debris. In some areas, floods have inundated the tracks. (AP)