The news came after more bodies were found following Friday's disaster at Meethotamulla on the city outskirts.
A number of those killed were children. Angry residents say their warnings of risks posed by the dump were ignored.
The 300ft (91m) high pile of rotting debris shifted after floods and a fire, destroying dozens of homes.
Residents had been demanding the dump's removal for years, saying it was causing health problems.
Sivakumar is looking for his missing daughter, but hopes are fading
One man who spoke to BBC Sinhala's Azzam Ameen said he had lost his wife and one of his children in the landslide.
Their bodies had been found - but Sivakumar was still looking for his other daughter.
The authorities do not know how many people were caught up in the landslide.
"We have not received adequate information to find out how many people were living in the area at the time," Brig Roshan Senaviratne told the BBC.
He said troops were having to dig down as deep as 20-30ft in places to look for bodies.
"Even with machines, it's difficult because the muddy soil means it takes time to complete the process."
Some 400 families have been moved to temporary shelters in schools, the AFP news agency reports.
The government has now announced the closure of the dump. Reports said 800 tonnes of waste were added to it every day.
Officials say rubbish will now be placed in two other sites.
Last month, a landslide at a rubbish dump in the Ethiopian capital, Addis Ababa, killed at least 113 people.