The government has deployed troops to evacuate people living on slopes or in flood-hit areas and the navy is helping clear canals in Colombo to stop low-lying areas including the parliament complex from flooding.
"We have placed troops at the disposal of the authorities to carry out rescue operations as well as relief work," Sri Lanka’s Defense Secretary Karunasena Hettiarachchi told reporters, according to AFP.
Disaster management center spokesman Pradeep Kodippili said nearly 5,000 families living in flooded areas had been moved to relief centers.
Thousands more have left flooded homes to move in with friends and relatives.
The official toll of eight could rise, with some areas still inaccessible after fallen trees and power lines blocked roads.
At least three flights were diverted from the main airport in Colombo on Monday and many schools in the capital remained closed.
The meteorological department said 262 mm (10.3 inches) of rain fell in the airport area in the 24 hours ending 5.30 a.m. Monday.
It has warned of further severe weather due to a depression in the Bay of Bengal and says rain could continue until Wednesday.