"One of our blessed battalions tried to hunt a head of one of America's infidels in Pakistan while he was returning from Fateh Jang, but God wanted him to survive," the statement said, referring to the town near the Pakistani capital where Friday's suicide attack on Shaukat Aziz took place.
Written in Arabic, the message was posted Saturday on an Islamic Web site known for carrying messages from Islamic militant groups.
It was not possible to verify the authenticity of the claim. The group calls itself the "Islambouli Brigades of al Qaeda." Lt. Khaled Islambouli was the leader of the group of soldiers who assassinated Egyptian President Anwar Sadat during a military parade in Cairo in 1981.
The statement said the attempted assassination was a response to Pakistani President Gen. Pervez Musharraf for his transferring wanted militants to the custody of the United States.
Addressing itself to Musharraf and the Pakistani government, the statement said "this operation yesterday will be followed by a series of painful strikes if you don't stop what you are doing by complying to the wicked Bush's orders."
The group said it was giving the government a "period of truce " to cease handing over detainees to America, failing which the militants "will behave in a different way."
The statement did not say how long the truce would last, but it warned that this message was "the last warning."
"Within the coming few days, our brigades will speak with the language of blood which is the only language you understand," the message added.
It accused Shaukat Aziz, currently the finance minister, of being "a follower of the wicked Bush and his cronies."
Pakistani police have said al Qaeda might have been behind Friday's attack. Musharraf says he believes al Qaeda was involved in two attempts to kill him in December.
Friday's attack came hours after Pakistan announced the capture of a senior al Qaeda terrorist, and a day after Pakistan said it was considering sending troops to Iraq.
Islamic militants are enraged at Musharraf's support for the U.S.-led war on terror. Al Qaeda No. 2 Ayman al-Zawahri called for his assassination earlier this year.