According to Reuters, 17 policemen were killed or injured in the attack.
The group did not give evidence backing its claim.
Earlier reports by Sri Lankan police and military said there were no casualties among troops. According to reports, three terrorists blew themselves up during a police raid, killing 15 people, including 6 children.
The military said explosives, detonators, "suicide kits," military uniforms and Daesh flags were recovered during the raid on a site believed to have been used for the manufacture of suicide vests.
On Saturday, Sri Lankan President Maithripala Sirisena banned the groups National Thawheedh Jamaath (NTJ) and Jamathei Millathu Ibrahim (JMI) which are suspected of being behind the Easter Sunday blasts, and are believed to have links with Daesh.
On 21 April, numerous bombings rattled Sri Lanka, leaving more than 250 people dead across the country. The government linked the attacks to supposedly Daesh-linked local terrorist group Thowheeth Jama'ath.
The Easter Sunday attacks were the worst the country has faced since the end of its 25-year civil war in 2009. Daesh reportedly claimed responsibility for the attacks on Tuesday.