The Islamic State on Saturday said its fighters were among those killed in the clashes with the Sri Lankan police. In a statement issued by Amaq, the group’s propaganda arm, it said that three of its fighters lured security forces to the house they were hiding in, before detonating suicide vests.

The Amaq statement was accompanied by a picture of Mr. Zaharan posing with one of his younger brothers, Rilwan. Members of Mr. Zaharan’s immediate family have followed his radical ideology for years. In an unverified video making its rounds on social media, Mr. Rilwan, Mr. Zaharan’s father and Mr. Zaharan’s brother in law are seen discussing martyrdom and jihadism, as children cry in the background. A wall of the room where the video was taken appears to match that of the safe house that was raided.

The Islamic State claim said that 17 members of the police were killed or wounded in the clashes, but that was disputed by the Sri Lankan authorities. The Islamic State has often exaggerated the numbers of dead and injured in its attacks.

Both Mr. Zaharan and Mr. Rilwan were named in an internal security report on April 11 that warned of a potential suicide attack on the country. The top echelons of the Sri Lankan government have been criticized for not heeding multiple alerts about a possible attack.

Also on Saturday, the Sri Lankan government banned the activities of National Thowheeth Jama’ath, the small extremist group founded by Mr. Zaharan. President Maithripala Sirisena made the decision under emergency regulations that were introduced soon after the attacks.