The statement was accompanied by a photo of Umar Farouk Abdulmutallab
An al-Qaeda regional offshoot says it was behind the failed attempt to bomb a US transatlantic flight last Friday, according to an internet statement.
Al-Qaeda in the Arabian Peninsula (AQAP) said the plot was to avenge US attacks on militants in Yemen, a US monitoring organisation reported.
A Nigerian man has been charged with attempting to set off an explosive device on a Amsterdam-Detroit flight.
It landed safely after the suspect was overpowered by passengers and crew.
The accused, Umar Farouk Abdulmutallab, had co-ordinated the plot with members of al-Qaeda in the Arabian Peninsula, said the statement, according to US monitor Site Intelligence.
Officials said at the weekend that the 23-year-old had told US investigators that al-Qaeda operatives in Yemen had supplied him with the bomb and trained him in how to detonate it.
Analysts say US intelligence has been aiding Yemeni forces, which carried out two airstrikes against al-Qaeda in the country this month, the second of which came on the eve of the attempted plane bombing.
Dozens of militants are reported to have died in the attacks.
In its internet statement, AQAP said: "We call on all Muslims... to throw out all unbelievers from the Arabian Peninsula by killing crusaders who work in embassies or elsewhere... [in] a total war on all crusaders in the Peninsula of [Prophet] Muhammad."
According to prosecutors, Mr Abdulmutallab tried to bring down the Northwest Airlines Airbus A330 using a device containing PETN, a high explosive.
The explosives were allegedly sewn in to the would-be bomber's underwear and officials believe tragedy was averted only because the makeshift detonator failed, before other passengers pounced on him.
The Washington-based IntelCenter, which monitors terror group communications, said that if AQAP was confirmed to be behind the attack it would be the first time the group had stuck outside the Saudi-Yemen area.
It said that even the call for such attacks marked "a significant escalation in the group's activities" which formed part of a larger series of "operational changes" since AQAP was formed by the merger of al-Qaeda branches in the two countries.
IntelCenter said the statement could mean AQAP and other regional militant groups "may no longer be content to just carry out attacks in their own backyards" but also to threaten the US.