"They tried to break the cordon and we opened fire and killed three people," Wanigasooriya said. He did not say if there were any troop casualties.
However, he said the military believed two of those killed were suspects wanted in connection with the shooting and injuring of a police officer last month in the island's north.
One of the men killed Friday was named as Kajadeepan Ponniah Selvanayagam, 31, who is better known as Gopi, Wanigasooriya told reporters in Colombo.
The government's information department separately described Gopi as a leader of the Liberation Tigers of Tamil Eelam (LTTE) in the north of the island, confirming he was among the three killed on Friday.
Wanigasooriya said the army had been able to locate the men's jungle hideout after the recovery on Thursday of three backpacks with food rations and medicines that the trio had abandoned nearby.He confirmed it was the first major shooting since government forces wiped out the Tiger leadership in May 2009 and declared an end to the 37-year-long war over a homeland for the ethnic Tamil minority.
- Pre-dawn raid -
The military carried out the pre-dawn operation in the sparsely populated jungles of Nedunkerni based on information from the police Terrorist Investigation Department, which was looking for the three men who were believed to be remnants of the Tamil Tigers, he said.
Wanigasooriya said that a soldier had also been killed in the island's north, but that death was unrelated to the jungle shootings.
Before the latest incidents, police had already appealed for information on Gopi who was accused of trying to reignite the Tigers movement.
They had offered a reward of a million rupees ($7,600) for information leading to his arrest.
He and another man identified as Nawaratnam Navaneethan, 36, had been accused of opening fire and injuring a police officer in the north of Sri Lanka last month. Navaneethan was also believed to be among those killed in Friday's army shooting.
The latest incident came a day after police announced they had detained 60 people, including 10 women, in connection with attempts to reactivate the Tiger movement.
The UN has estimated that at least 100,000 people were killed in Sri Lanka's Tamil separatist conflict between 1972 and 2009.
The UN rights body last month called for an international probe into allegations that thousands of civilians were killed by government forces as well as Tamil Tiger rebels.
Colombo has rejected the UN Human Rights Council resolution and made clear it will not cooperate with any probe after insisting that its troops did not kill a single civilian.
Sri Lanka is also under intense foreign pressure to scrap draconian anti-terror laws, but Colombo maintains that they need the extra ordinary powers to deal with a possible resurgence of terrorism.