The terrorist group released statements in several languages through its central media body praising the atrocity, claiming more than 100 "crusaders" were killed or wounded at the "shameless" concert.
"With Allah's grace and support, a soldier of the Khilafah [caliphate] managed to place explosive devices in the midst of the gatherings of the crusaders in the British city of Manchester," said the English version.
It suggested the atrocity was not a suicide attack, despite police statements saying the perpetrator died at the scene, and did not name him as a "martyr".
Isis said the attack aimed to terrorise "infidels...in response to their transgressions against the lands of the Muslims".
The release of a lengthy official claim so quickly after the bombing suggested the attacker had been in direct contact with Isis militants.
The group's supporters had been circulating an unverified video claiming to show a masked English-speaking militant claiming responsibility for the Manchester attack.
But analysts pointed out that a flag positioned behind the man was not the symbol most commonly associated with Isis, which he did not refer to by its usual name. It was unclear when it was filmed.
The blast killed 22 people and injured dozens more at an Ariana Grande concert on Monday night.
Ian Hopkins, the Chief Constable of Greater Manchester Police, said investigators believe the attack was carried out by a lone suicide bomber “carrying” a homemade device.
“The priority is to establish whether he was acting alone or as part of a network,” he added.
“The attacker, I can confirm, died at the arena. We believe the attacker was carrying an improvised explosive device which he detonated causing this atrocity.”
It followed calls by Isis and other terror groups to attack "disbelievers" in the West.
Isis has been periodically releasing detailed guidance on how to carry out terror attacks in countries targeting its militants in Syria and Iraq, including bomb-making instructions.
The most recent edition of its Rumiyah propaganda magazine listed concert halls among “ideal target locations” for attacks.
Analysts have warned that the group may increasingly turn to “soft targets” with large crowds, as seen in Westminster, Stockholm, Nice and Berlin, rather than protected areas with a high security presence.
Explosive devices using homemade triacetone triperoxide (TATP) have become a signature of the group’s largest European attacks in Paris and Brussels, and has been discovered in several foiled plots.
The Manchester attack took place on the fourth anniversary of the killing of Fusilier Lee Rigby in Woolwich, which was inspired by al-Qaeda propaganda on avenging civilian casualties in the Middle East.
Theresa May said security services had identified the attacker but it was too early in the investigation to release his name.
“The police and emergency services have as always acted with great courage and on behalf of the country I want to express our gratitude to them - they acted in accordance with the plans they have in place and the exercises they conduct to test those plans and they performed with the utmost professionalism,“ the Prime Minister added.
At least one person, a 23-year-old man from Manchester, has so far been arrested in connection with the bombing.
In a rare statement, the director general of domestic intelligence agency MI5 said staff were "revolted by the disgusting terrorist attack.
“We remain relentlessly focussed, in numerous current operations, on doing all we can to combat the scourge of terrorism and keep the country safe,” Andrew Parker added.
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