As the heavily-armed men opened fire on troops, a civilian caught in the middle got killed.
As the clashes intensified, three men are believed to have set off explosives.
In a statement published early Sunday through the its propaganda 'Amaq' news agency, the ISIS said that it gave their noms du guerre as Abu Hammad, Abu Sufyan and Abu al-Qa'qa, the Colombo Gazette reported.
It said they opened fire with automatic weapons and after exhausting their ammunition, detonated on them their explosive belts.
Six children and three women were among 15 people killed when the militants opened fire and blew themselves up during the gun battle with security forces.
A police spokesman said that three suspected suicide bombers were among the 15 dead.
A huge cache of explosives was also recovered from the spot.
Officials have recovered detonators, suicide kits, army uniforms and ISIS flags.
Nine suicide bombers carried out a series of devastating blasts that tore through three churches and three luxury hotels on the Easter Sunday, killing 253 people.
The ISIS claimed the attacks, but the government has blamed local Islamist extremist group NTJ for the attacks.
President Maithripala Sirisena said Friday that over 130 suspects linked to the ISIS have been operating in the country.
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