In a statement received by Aljazeera on Friday, the group also claimed responsibility for a number of operations targeting the US occupation forces in Baghdad.
Against the backdrop of a distinctly Shia flag the group said "its operations against the foreign forces will continue until the last soldier leaves Iraqi territory."
It also said it would not target Iraqi officials or policemen "as long as they show keenness to serve the Iraqi people and maintain security."
The attack will cause concern to coalition forces who have just succeeded in pacifying a rebellion led by Shia cleric Muqtada al-Sadr whose forces had bucked the trend of a largely cooperative Shia community.
The rockets were fired at two central Baghdad hotels frequented by foreigners.
Aljazeera reported that at least three people were wounded in the attack.
A US soldier and an eyewitness said plumes of smoke rose into the air when the rockets struck the Sheraton hotel .
A minivan drove up to within range of the heavily guarded Sheraton and started popping off rockets, said a US army captain who gave his name as Mayo.
The attackers were part-way through launching a cache of about nine home-made projectiles when the remaining ordnance exploded in the vehicle, Mayo said.
Baghdad's Sheraton hotel is
frequented by many foreigners
Aljazeera correspondent in Baghdad, Laila al-Shaib said an Iraqi police source said a similar incident took place at Wathiq Square but the information has not been officially confirmed.
A witness said a rocket smashed into the Sheraton hotel's 10th floor and a second projectile crashed into the nearby Baghdad Hotel's parking lot.
A local resident said the attack happened at about 05:50 (02:50 GMT). "I heard a very loud explosion," recalled Duraid Aziz, aged 38.
At least two loud explosions shook the areas and black smoke belched into the sky.
The Sheraton and Palestine hotels are occasional targets of rocket and mortar attacks.