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.
"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.
The Tamil Tigers, listed as a terror organization by the United States and the European Union, have carried out more than 240 suicide bombings and countless other attacks. 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 the Tamil Tigers 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 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 17 people were killed and 36 others injured. At a nearby hospital, residents searched for 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.
Earlier Wednesday, a handicapped suicide bomber blew herself up at Sri Lanka's social services ministry in the heart of Colombo, the military said.
The attack targeted the offices of Douglas Devananda, the minister of social services and the leader of the Eelam People's Democratic Party, an ethnic Tamil party considered a rival to the rebels, the military said.
Devananda, the target of repeated assassination attempts, was not injured in the attack, but the blast killed one of his staff members and injured two others, military officials said. The bomber was also killed.
"This was an attempt to kill the minister," Nanayakkara said, blaming the Tamil Tigers.
Ilanthirayan, the rebel spokesman, said he was unaware of the blast.
The attacks came a day after 22 civilians - including 11 schoolchildren - were killed in separate attacks inside rebel-controlled territory in northern Sri Lanka. The rebels blamed the military for the attacks.
The military denied responsibility for the roadside bombing that killed the children and two others, but said it was behind the bombing of a rebel radio station that killed nine people.
Also Tuesday, the rebels' top leader, the reclusive Velupillai Prabhakaran, blamed the international community for the worsening violence in the country, saying military, economic and diplomatic assistance to the government was feeding the bloodshed.
"This partisan and unjust conduct of the international community has severely undermined the confidence our people had in them. And it has paved the way for the breakdown of the cease-fire and the peace efforts," the rebel leader said in his annual address to the Tamil people.
He also accused the government of continuing "on the path of violence. It only desires to find a solution to the Tamil question through military might and oppression," he said.
The military also said it killed one rebel in an attack Wednesday on a Tamil Tiger bunker and another in fighting in the north on Tuesday.
The import of liquefied natural gas from the United States will not grow, even if Germany exits the Nord Stream-2 project, German Minister of Economy and Energy Peter Altmeier said