The group said on its website on Monday that the attempt had been carried out to avenge US operations in Yemen.
Umar Farouk Abdulmutallab, a Nigerian, attempted to light an explosive device on a flight from Amsterdam to Detroit with nearly 300 people onboard.
The group said it had provided Abdulmutallab with the device, but that a technical fault prevented it from detonating.
Abdulmutallab, who was overpowered by passengers on the flight, is in US custody having been charged with the attack.
According to a chargesheet prepared by prosecutors, Abdulmutallab tried to bring down the aircraft using a device containing PETN, also known as pentaerythritol, an explosive.
The explosive material was allegedly sewn into his underwear.
Abdulmutallab, who suffered burns in the incident, was moved from a hospital to a federal prison west of Detroit on Monday.
Meanwhile, Barack Obama, the US president, has ordered a review of how travellers are placed on watch lists and the screening procedures of air passengers following the failed bid to blow up the airliner.
Speaking while on vacation in Hawaii on Monday, Obama said: "We will not rest until we find all who were involved and hold them accountable."
Abdulmutallab, a former student in London, was added to a watch-list of some 550,000 names last month after his father told US embassy officials in Abuja that he was concerned by his son's increasing radicalism.But he remained off a short-list of 18,000 names from which the no-fly list of 4,000 is selected and flew from Lagos to Amsterdam on Christmas Eve and on to Detroit the following day with a valid US visa.
"There is a series of databases that list people of concern to several agencies across the government. We want to make sure information-sharing is going on," Robert Gibbs, a White House spokesman, said.
"The president has asked that a review be undertaken to ensure that any information gets to where it needs to go, to the people making the decisions."
Obama has also ordered a second review to examine how "an individual with the chemical explosive he had on him could get onto an airliner in Amsterdam and fly into this country," Gibbs said.
With questions now being asked about security measures, air travellers in the US were being told to check-in four hours ahead of scheduled departure times, while bomb-sniffing dogs were visible at airports across the country.
Once on board, many passengers were told they would be unable to hold coats or blankets in their laps and would not be allowed to enter aircraft restrooms for the last hour of their flights.
In Nigeria, Abdulmutallab's family promised their full co-operation with security agencies and said his recent behaviour had been "completely out of character".
In a statement, the family said it had grown so concerned at the lack of contact in recent weeks that his parents had contacted security agencies.
"Before then, from very early childhood, Farouk, to the best of parental monitoring, had never shown any attitude, conduct or association that would give concern."
Relatives have said previously that Abdulmutallab, son of leading Nigerian businessman Umar Abdulmutallab, had broken contact with them several weeks ago after announcing that he was studying in Yemen.
According to The New York Times, Abdulmutallab told FBI agents he was connected to an al-Qaeda affiliate, which operates largely in Yemen and Saudi Arabia, by a radical Yemeni cleric whom he contacted online.
But Janet Napolitano, Obama's top security official, said there was "no indication" Abdulmutallab was acting as part of a larger plot and warned against speculating that he had been trained by al-Qaeda.