At least 20 people were killed and 68 others injured in the explosion at a bus station in Dambulla.
"We have information that two people got off the bus before the bomb went off," Kingsley Ekanayaka, police deputy inspector-general, said.
"We are trying to track them down. A search is under way."
Mahinda Rajapakse, the president, has condemned Saturday's bombing and urged Sri Lankans not to be provoked by what he called the "savage attack" blamed on Tamil Tigers separatists.
Security forces have been placed on high alert as Sri Lanka prepares to mark the 60th anniversary of independence form Britain.
NK Illangakoon, the police spokesman, defended holding the celebrations despite fears of more attacks.
"We can't allow terrorists to disrupt our independence day celebrations," he said. "We are providing maximum security."
About 4,100 troops, along with tanks and multi-barrelled rocket launchers, will be deployed for a procession along the seafront.
Fighting between the Sri Lankan military and the the Liberation Tigers of Tamil Eelam (LTTE) has escalated since the government scrapped a six-year ceasefire last month, saying the rebels were using it to rebuild and re-arm.
The military said on Sunday that it had killed at least 46 LTTE fighters in recent clashes in the northern areas of Jaffna, Vavuniya and Polonnaruwa and Mannar in the northwest.
Meanwhile, the Tamil Tigers accused the military of blowing up a school bus inside LTTE-held territory last month, which killed 18 people, including 11 children.