The posting on a website came just hours after the series of deadly blasts in the Red Sea resort.
The group, calling itself the Abd Allah Azzam Brigades, al-Qaida, in Syria and Egypt, said that its "holy warriors targeted the Ghazala Gardens Hotel and the Old Market in Sharm al-Shaikh".
The authenticity of the statement could not be verified.
The group is one of two that claimed responsibility for the 7 October bombings in the Sinai Peninsula atTaba and Ras Shitan that killed 34 people.
"Your brothers, the holy warriors of the martyr Abd Allah Azzam Brigades succeeded in launching a smashing attack on the Crusaders, Zionists and the renegade Egyptian regime in Sharm al-Shaikh," the statement read.
"We reaffirm that this operation was in response to the crimes committed by the forces of international evil, which are spilling the blood of Muslims in Iraq, Afghanistan and Chechnya.
"We declare it loud and clear that we will not be frightened by the whips of the Egyptian torturers and we will not tolerate violation of our brothers' land of Sinai," the statement added in an apparent reference to tourists who travel from neighbouring Israel to Sinai Peninsula for holidays.
Abd Allah Azzam
The Abd Allah Azzam Brigades are apparently named after Abd Allah Azzam, a Palestinian who led Islamic fighters in Afghanistan and was killed in 1989 by a roadside bomb, and was regarded as the one-time spiritual mentor of al-Qaida chief Osama bin Laden.
Azzam studied Islamic theology in Egypt before travelling to Saudi Arabia where he lectured in Islamic law.
During the Soviet invasion of Afghanistan, Azzam was financed by Saudi Arabia to establish camps for Muslims who joined the fight against the Russian forces.