President Maithripala Sirisena flew to a central tea-growing area where images taken from a helicopter showed floodwaters engulfing entire villages and forested hills deluged with reddish mud.
“The loss is devastating,” the president posted on Twitter.
The Disaster Management Centre’s updated toll came after bodies were pulled out of the mud in the central village of Aranayake and neighbouring Bulathkohupitiya.
“A total of 37 people have been killed, 28 wounded… in weather-related incidents in the past three days,” DMC spokesman Pradeep Kodippili said.
The president met with people who had lost their loved ones as well as seen their homes destroyed, an official who travelled with him told AFP.
Sirisena has ordered troops to help evacuate people living on slopes or in flood-hit areas, while the navy and the air force have also been called in to help with relief operations.
In the area worst hit by landslides, 134 people were still unaccounted for. “We have got complaints from relatives about their loved ones missing,” a police officer in the area told AFP by telephone.
In total 155 people are still missing.
Meanwhile about 150 people living above the landslide-hit area have been rescued, military spokesman Jayanath Jayaweera told reporters.
“Army commandos rescued all of them this morning,” Jayaweera said, adding that 266 troops in total have been deployed for relief and rescue operations in the worst-affected central district of Kegalle.
Kegalle was prone to landslides and many people living there had fled their homes after the rains, DMC’s Kodippili said.
He countered a tweet from the Sri Lankan Red Cross that more than 200 families were missing, saying most had been accounted for and the death toll was not expected to rise significantly.
Sri Lanka Red Cross spokesmen Mahieash Johnny told AFP that there had earlier been confusion about the number of people missing.
But Johnny said the latest updates from the scene suggested that an estimated 225 families were affected by the landslides and “most of those families have moved to four relief camps in the area”.
Police said many residents had fled the tea-growing and farming area before the landslides hit.
Over 350,000 people have been hit by flooding in Sri Lanka and 223,000 are sheltering in state-run welfare centres.
The meteorological department said the heavy rains were caused by a depression in the Bay of Bengal and were expected to subside on Wednesday.