The army told the BBC that 134 people remained unaccounted for after mudslides hit three villages in central Kegalle district.
At least 14 bodies have been recovered so far. Another three bodies were found elsewhere in the district.
Disaster officials say about 150 people have been rescued but more than 60 houses have been buried by mud.
Landslides and flooding caused by three days of torrential rain in Sri Lanka have killed at least 37 people in total, according to official figures.
Nearly 350,000 people have been displaced.
The huge landslide happened near the town of Aranayake late on Tuesday afternoon. Rescuers say they are having difficulty getting heavy equipment to the worst-hit places.
Images show a vast stretch of hillside which has sheared off, sending mud, rocks and trees crashing down on the villages of Siripura, Pallebage and Elagipitya.
A huge section of the mountainside broke away, covering villages below – AFP
“I heard a huge sound like a plane crashing into the earth,” said one villager in Siripura, Associated Press reports.
“I opened my door. I could not believe my eyes, as I saw something like a huge fireball rolling down the mountain.”
The Sri Lankan Red Cross tweeted that more than 200 families were feared buried in the mud, but later said reports suggested many of the missing had made their way to relief camps.
Maj Gen Sudantha Ranasinghe, who is in charge of rescue operations in Aranayake, told BBC Sinhala: “There are around 1,100 people now in the four camps we have set up.”
Police confirm they have also recovered three bodies at the village of Bulathkohupitiya, scene of another landslide in the district. Sixteen people are also missing.
President Maithripala Sirisena is visiting the Kegalle area to meet victims’ families.
Meanwhile, officials in other badly-hit parts of the island have appealed to the public to send water, dry food rations and sanitary items for those affected.
In southern India the authorities have been put on alert as the heavy rains are forecast to move on to Chennai and parts of Tamil Nadu and Pondicherry.
Fishermen have been warned against going to sea and rescue teams are on standby.
At least 280 people died in a month of heavy rains and floods in Chennai and other parts of Tamil Nadu last year. The rains, the heaviest there in a century, were blamed on climate change although city officials were also criticised for being unprepared. Other parts of India have been suffering a severe drought in recent weeks.
