The garbage dump came crashing down on neighbouring homes after catching fire, burying at least 145 houses late on Friday.
Hopes of finding anyone alive under a collapsed mountain of garbage in the capital Colombo faded Sunday as the death toll reached 21, police said.
The 90-metre (300-foot-high) dump collapsed after flames engulfed it late on Friday, the first day of the nation's new year, and witnesses said around 145 homes that were destroyed.
"The rescue is fast becoming a recovery operation," a senior police official at the site said. "It is difficult to imagine anyone could survive under these toxic conditions."
The police said they were investigating whether the landslide was natural or man-made.
"We heard a massive sound. It was like thunder. Tiles in our house got cracked. Black water started coming in," said one survivor identified himself as Kularathna.
"We tried to get out but we were trapped inside. We shouted for help and were rescued later."
President Maithripala Sirisena ordered hundreds of troops to search for survivors and bolster rescue efforts of the fire department.
Wickremesinghe said Japanese Prime Minister Shinzo Abe offered help with the recovery effort and a technical team would be sent to Sri Lanka to evaluate the situation.