"Troops retaliated and raided the safe house where a large cache of explosives had been stored," military spokesman Sumith Atapattu said in a statement and added that three explosions were triggered and gunfire began as security forces approached the location.
Among the dead are three women and six children. Atapattu disclosed that the suspected premises is believed to be a refuge for an Islamic State group in Kalmunai and the occupants are linked to the bombings at three churches and four hotels.
Authorities say the police officers, who were acting on information from intelligence officials, found 150 sticks of blasting gelatin as well as 100,000 small metal balls used to amplify shrapnel dispersion in explosions in the vicinity of the premises.
The shootout started late Friday in the coastal town of Sammanthurai, which is located some 200 miles from the Sri Lankan capital, Colombo.
Over 250 people died in the coordinated suicide bombings that have prompted Catholic churches across the country to cancel all Sunday masses until further notice.
Police have, so far, detained at least 76 people, including foreigners from Syria and Egypt, in their investigations into the Easter attack.
Official reports disclosed that the perpetrators of the ghastly bombings were well-educated individuals who hailed from affluent middle- and upper-class families. Two of the suspected bombers were sons of Sri Lanka's top spice exporter, who was taken into custody and questioned by police.