The claim, issued through the group's AMAQ news agency, came shortly after Sri Lanka said two domestic Islamist groups, with suspected links to foreign militants, were believed to have been behind the attacks at three churches and four hotels that also wounded about 500 people.
Three sources with direct knowledge of the matter told Reuters that Sri Lankan intelligence officials had been warned hours earlier by India that attacks by Islamists were imminent. It was not clear what action, if any, was taken.
Sri Lanka's prime minister, Ranil Wickremesinghe, told a news conference investigators were making progress in identifying the perpetrators.
"We will be following up on IS claims, we believe there may be some links," he said.
The government has said at least seven suicide bombers were involved.
In a statement, Islamic State named what it said were the seven attackers who carried out the attacks. It gave no further evidence to support its claim of responsibility.
Earlier, junior minister for defence Ruwan Wijewardene told parliament two Sri Lankan Islamist groups - the National Thawheed Jama'ut and Jammiyathul Millathu Ibrahim - were responsible for the blasts, which detonated during Easter services and as high-end hotels served breakfast.
Wickremesinghe said the militants had tried to attack another hotel but had failed.
Sri Lankan government and military sources said a Syrian had been detained among 40 people being questioned over the bombs.
Most of the dead and wounded were Sri Lankans, although government officials said 38 foreigners were killed. That included British, US, Australian, Turkish, Indian, Chinese, Danish, Dutch and Portuguese nationals.
The UN Children's Fund said 45 children were among the dead.
Footage on CNN showed what it said was one of the bombers wearing a heavy backpack. The man patted a child on the head before entering the Gothic-style St. Sebastian church in Katuwapitiya, north of Colombo. Dozens were killed there.
'RETALIATION'
Wijewardene said investigators believed revenge for the March 15 killing of 50 people at two mosques during Friday prayers in the New Zealand city of Christchurch was the motive.
"The initial investigation has revealed that this was in retaliation for the New Zealand mosque attack," he said.
He did not elaborate on why authorities believed there was a link to the New Zealand bloodshed, unleashed by a lone gunman.
The bombs brought a shattering end to a relative calm that had existed in the Buddhist-majority Indian Ocean island since a civil war against mostly Hindu, ethnic Tamil separatists ended 10 years ago, and raised fears of a return to sectarian violence.
Pressure is likely to mount on the government over why effective action had not been taken in response to warnings from India about a possible attack on churches by the little-known National Thawheed Jama'ut group.
Indian intelligence officers contacted their Sri Lankan counterparts two hours before the first attack to warn of a specific threat on churches, one Sri Lankan defence source and an Indian government source said.
Another Sri Lankan defence source said a warning came "hours before" the first strike.
Sri Lanka's presidency and the Indian foreign ministry both did not respond to requests for comment on the warnings.
A government minister had said on Monday that Wickremesinghe had not been informed about a warning and had been shut out of top security meetings because of a feud with President Maithripala Sirisena.
Wickremesinghe dismissed any suggestion that the rift with the president had hampered coordination on security, saying although they had had differences they had been thrashed out.
Sirisena fired Wickremesinghe last year only to be forced to reinstate him under pressure from the Supreme Court.
Tuesday was a day of mourning and more than 1,000 mourners gathered for a mass funeral at St. Sebastian church in the coastal city of Negombo, just north of the capital, Colombo, where more than 100 parishioners were killed on Sunday.
The ceremony began with prayers and singing under a tent put up in the courtyard of the church, which had most of its roof torn away by the blast.
Pall-bearers wearing white carried in wooden coffins one by one, followed by distraught relatives.
Cardinal Malcolm Ranjith, the archbishop of Sri Lanka who led the service, urged other churches to delay memorials amid fears that more bombers may be at large.
The government also said it had blocked online messaging services to stop the spread of inflammatory rumours that it feared could incite communal clashes.
"We blocked WhatsApp because we didn't want to take a chance," Wickremesinghe told reporters.
The FBI is assisting Sri Lankan authorities with their investigation of the bomb attacks, a spokeswoman for the US law enforcement agency said on Tuesday.
The Washington Post earlier had reported that the FBI had offered expertise to test evidence and that analysts were scouring databases for information regarding the attacks.