Over 100 houses were completely destroyed and more than 600 people fled in the aftermath of the fire and the collapse of the dump in Meetotamulla area in Kolonnawa, near here, police said.
17 people, including four children, were killed and 14 others injured in the incident that happened yesterday, officials said.
More people were feared to be trapped as the military struggled to clear the rubble and rescue people or recover bodies.
Prime Minister Ranil Wickremesinghe issued an apology on behalf of the government to the victims.
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"We had all plans in place to relocate the garbage dump at Meetotamulla. But the tragedy struck before we could put them into action. We apologise for the government's inability to complete the task before the disaster," he said.
The residents near the dump had been protesting for months, demanding that the garbage mound be relocated.
The authorities, however, claim that they had given enough warning to the slum dwellers to relocate themselves.
The minister said it was only a few weeks back that agreements had been signed to begin waste to enegry projects at the dumping site.
The mountain of garbage caught fire and collapsed on dozens of homes as the residents were celebrating the traditional New Year.
Police said the true scale of the damage remained unclear.
Sri Lanka's Parliament was recently warned that 23 million tonnes of garbage at Kolonnawa dump was a serious health hazard. About 800 tonnes of garbage is being added to the dump on a daily basis.