The death toll from Friday's collapse in the capital Colombo has risen to 26, including six children, the army says.
The 300ft (91m) high pile of rotting debris shifted after floods and a fire, destroying dozens of homes.
Residents had demanded for years the removal of the dump, saying it was causing health problems.
About a thousand people are thought to have been displaced by the disaster.
The government has now announced the closure of the Meethotamulla dump. Reports said 800 tonnes of waste were added to it every day.
President Maithripala Sirisena ordered hundreds of troops to search for survivors and bolster rescue efforts of the fire department.
The army said the operation would continue until all the missing were found.
"We expect we could complete this in the next 72 hours," spokesman Brig Roshan Senaviratne told the BBC.
Meanwhile, funerals for most of the victims were being held on Sunday.
Among them were four children, aged between 11 and 15, medical officials told AFP news agency.
Angry residents have barred politicians from visiting the site of the collapse.
"It's very unfortunate that no-one listened to us. Now, after so many deaths, politicians are saying they will stop dumping garbage. These are murders, we will take legal action," resident Nuwan Bopage told the BBC.
More than 600 people had been given temporary shelter at a government-run school in the area, AFP added.
The collapse occurred as many people were marking Aluth Avurudda, or the Sinhalese New Year, a major public holiday across Sri Lanka.
With the closure of the Meethotamulla dump, officials said the rubbish would 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.
Hopes of finding survivors under a collapsed rubbish dump in Sri Lanka are fading as anger builds among residents who say their concerns were ignored.