It would be a rare attack by the separatist group on a purely civilian area in recent years, though civilians have been killed in previous Tamil Tiger attacks on government and military targets.
The military blamed the rebels for the blast.
"We know that the attack bears all the hallmarks of the LTTE. It is nobody else but the LTTE," military spokesman Brig. Udaya Nanayakkara said, referring to the group by its formal name, the Liberation Tigers of Tamil Eelam.
Rebel spokesman Rasiah Ilanthirayan did not answer repeated calls from The Associated Press seeking comment.
Earlier in the day, a female suicide bomber sent by Tamil Tiger rebels killed one person and wounded two others in an unsuccessful attempt to kill a Cabinet minister in his office in Sri Lanka's capital of Colombo, the military said.
The blast Wednesday evening occurred just outside the four-story No Limits store in Nugegoda as commuters crowded a nearby bus stop during the evening rush hour, officials said.
The powerful explosion shattered the department store's windows and sent piles of crumbled concrete pouring onto the bloodstained sidewalk, according to an Associated Press photographer at the scene. Crumpled and charred parts of motorcycles and three-wheeled taxis were scattered nearby.
Police and firefighters were digging through the rubble in a search for more bodies.
"I was on the top floor of a shoe shop with my wife and child when I heard a big blast and there were glass pieces all over us" local resident A. Jayasena told AP Television News. "As we ran away, I saw the entrance of the No Limit shop burning, and in the midst of it a schoolgirl on the floor trying to get up and then falling back again."
Jayasena and his daughter suffered minor injuries, while his wife was in a hospital being treated for more serious wounds, he said.
The military said in a statement that at least 16 people were killed and 37 others injured. At a nearby hospital, residents came in search of missing relatives. One girl who suffered a broken arm in the attack sat with her mother as she received treatment.
The bomb may have exploded when a security guard at the mall became suspicious about a parcel and tried to open it, a defense official said, speaking on condition of anonymity because he was not authorized to talk to the media.
However, police at the scene said the explosives may have been in one of the three-wheeled taxis that were destroyed.
The Tamil Tigers have been fighting since 1983 to create a separate homeland for Sri Lanka's minority ethnic Tamils following decades of discrimination by governments controlled by the Sinhalese majority. The fighting has killed an estimated 70,000 people.
In the past two years, rebel bombers had avoided deliberately targeting civilians, though they have ambushed military convoys at crowded places, causing many civilian deaths.
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