In a statement released by its Amaq propaganda agency, the group said it was targeting citizens of countries bombings its territories and Christians.
“A security source told Amaq agency the perpetrators of the attack targeting the citizens of [US-led] coalition countries and Christians in Sri Lanka were Islamic State fighters,” it said.
The wording of Isis's claim is similar to that for previous atrocities that were thought to be inspired by the group but not directly orchestrated by it.
The statement contained no further information or evidence.
It came after Isis supporters circulated unverified photographs claiming to show three of the suicide bombers who targeted churches and hotels on Easter Sunday.
They showed the men posing with a knife and guns in front of Isis’s black flag, captioned with the names Abul Muktar, Abu Ubaida and Abul Barra.
Sri Lankan authorities had attributed the atrocities to a little-known local Islamist group called National Thowheed Jama’ath, which was previously known for vandalising Buddhist statues.
But the president asked for foreign assistance to track down the bombers’ international links on Monday, because of intelligence reports “indicating that foreign terrorist organisations are behind the local terrorists”.
The targeting of churches and hotels popular with foreign tourists is a technique recently used by Isis and al-Qaeda affiliates.
But attacks organised or coordinated by Isis have been claimed faster, with detail, and sometimes seen the group put out gory videos and footage from the scene.
Isis released its claim shortly after Sri Lanka’s defence minister said the attacks were “carried out in retaliation” for shootings that left 50 Muslims dead at mosques in New Zealand last month.