Military spokesman Brigadier Ruwan Wanigasooriya said troops killed the three, including a man they identified as a local leader of the Tigers, as they tried to escape a military cordon in a jungle area of the former war zone to the south of Jaffna.
"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 j