It said the aim of the Marriott attack was to kick "American crusaders" out of Pakistan and stop them interfering in the government, the military and the media, as well as security, religious and other institutions in Pakistan.
It also said that some 250 US marines had been killed in the attack, together with many officials from Nato and other countries involved in attacks on Muslim interests in Pakistan and Afghanistan.
However, almost all of the dead were Pakistanis. The Czech ambassador to Pakistan, one Vietnamese, a German and an American were among the dead, with an American and a Danish intelligence officer missing, presumed dead.
The Fidayeen-e-Islam group are reported to operate out of the tribal region of Waziristan along the Afghan border.
The BBC's Syed Shoaib Hasan in Islamabad reports that they are believed to have close links to the Tehrik-e Taleban Pakistan, a loose alliance of militants led by Baitullah Mehsud, who the previous government blamed for the assassination of Benazir Bhutto.
Our correspondent says the Fidayeen-e-Islam is believed to be composed largely of former members of the militant group Jaish-e-Mohammad, which is banned in Pakistan and was involved in several high-profile incidents there.
These include the murder of US journalist Daniel Pearl and an attack that nearly killed President Pervez Musharraf in December 2003.
In Monday's taped message the group said that if missiles were the technology of the US, then suicide attacks were the group's technology.
The heavily guarded Islamabad Marriott was attacked at about 2000 (1500 GMT) on Saturday.
The BBC's Damian Grammaticas tours the site of the bomb attack
CCTV footage of the moments before the blast show a six-wheeler lorry ramming the security barrier at the hotel gate.
The bomb - believed to have been detonated in the lorry - left a six-metre (20ft) crater.
Residents of Islamabad have told the BBC there is now a climate of fear in the city with people too scared to go out.
The blast has prompted British Airways to cancel some flights to Pakistan "in light of the security situation".
The Marriott was the most prestigious hotel in the capital, located near government buildings and diplomatic missions. It was popular with foreigners and the Pakistani elite.
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