In a statement published early Sunday by the extremists' Aamaq news agency, IS gave their noms du guerre as Abu Hammad, Abu Sufyan and Abu al-Qa'qa.
It says they opened fire with automatic weapons and "after exhausting their ammunition, detonated on them their explosive belts."
IS falsely claimed their militants killed 17 "disbelievers" in the attack. The militants often exaggerate their claims.
The claim carried a photograph of two men before an IS flag, one carrying a Chinese variant of the Kalashnikov rifle like the one found at the scene, another smiling.
Sri Lanka's military says the gunfight Friday night in Ampara District left 15 dead, including six children.