Another five people are missing across the island, parts of which have been underwater since Sunday, a spokesman for the Disaster Management Centre said.
"Over 200,000 individuals have been displaced by the floods and are being looked after at several welfare centres," Pradeep Kodippili said.
The northern district of Kilinochchi received the highest rainfall of 373 millimetres in the 24 hours ending Tuesday morning -- more than a quarter of the annual average rainfall in the region.
The government has deployed troops to evacuate people living on slopes or in flood-hit areas and the navy and the air force have also been called in to help with relief operations.
The meteorological department says the heavy rains could continue until Wednesday.
Meanwhile, the floods and landslides have forced more than 130,000 people to leave their homes for higher ground.
Troops have launched rescue operations in inundated areas of the Indian Ocean island, with boats and helicopters deployed to pull to safety more than 200 people trapped in the northwestern coastal district of Puttalam, officials said.
"This is the worst torrential rain we have seen since 2010," said Pradeep Kodippili, a spokesman for the country's disaster management centre, adding that many incidents were still flowing in from the 19 districts hit, among Sri Lanka's 25.
Flooded roads and fallen trees led to traffic jams in Colombo. Trains were halted as water submerged railway tracks, officials said. Families living beside rivers used boats to negotiate their way to safety.
A DMC bulletin reported a total of eight deaths, ascribing four to landslides, and one each to floods, electric shock, a lightning strike and an uprooted tree.
But it did not reflect three further deaths in a landslide in the central district of Kandy, the DMC spokesman added.
Eight people have reported missing and nine have been injured, the bulletin said.
Transport disruptions included the diversion of three Colombo-bound international flights, which went instead to Sri Lanka's second airport in its south and Kochi airport in nearby south India.
Flooding and mass displacement due to torrential rains are common in Sri Lanka.
The rains are expected to disperse slightly, weather officials said, as a low pressure area in the Bay of Bengal that brought them moves away, but strong winds will persist a few days longer.
