The bombs, which hit at about 9 p.m. at the Grand Hyatt, Radisson SAS and Days Inn hotels, killed at least 56 people and wounded more than 115 other people.
The al Qaeda claim, posted on a militant Internet site, said Jordan became a target because it was "a backyard garden for the enemies of the religion, Jews and crusaders ... a filthy place for the traitors ... and a center for prostitution."
The statement is attributed to the spokesman for al Qaeda in Iraq, a group led by the Jordanian-born Abu Musab al-Zarqawi. Its authenticity could not be immediately determined, but it appeared on a site routinely used by al Qaeda operatives.
"I think there is no question but they (al Qaeda) were responsible," said terrorism expert Neil Livingstone on CBS News' The Early Show. "Whether it's an affiliate group such as the al-Zarqawi movement in Iraq, which is probably attempting right now to open a second front, or whether it got some direction actually from al Qaeda itself, it's really not material to this. It's all part and parcel to the same movement."
The statement said the attacks put the United States on notice that the "backyard camp for the crusader army is now in the range of fire of the holy warriors."
CBS News correspondent Kimberly Dozier reports that al-Zarqawi has become Osama bin Laden's top lieutenant in Iraq, a mastermind of some of the deadliest violence the region has ever seen. His path towards terror started at a Jordanian prison. There he was first indoctrinated by militant extremists, which led to his alleged involvement in the 2002 killing of Lawrence Foley, then executive officer of US Aid in Amman, outside the official's home in Amman.
In February, U.S. intelligence indicated that bin Laden was in contact with al-Zarqawi, enlisting him to conduct attacks outside of Iraq, noted another U.S. counterterrorism official, who also spoke on condition of anonymity. Jordan has arrested scores of Islamic militants for plotting to carry out attacks and has also sentenced many militants to death in absentia, including al-Zarqawi.
The first and possibly the worst of the three bombings occurred at the Radisson Hotel, reports CBS News correspondent David Hawkins. A suicide bomber blew himself up in the in middle of a wedding party there moments before the arrival of the bride and bridegroom.
"We thought it was fireworks for the wedding but I saw people falling to the ground," said Ahmed, a wedding guest at the five-star Radisson who did not give his surname. "I saw blood. There were people killed. It was ugly."
A government spokesman said the victims included 15 Jordanians, five Iraqis, one Saudi, one Palestinian, three Chinese, one Indonesian; 30 others hadn't been identified. A State Department official says so far there are no known American casualties.
The United Nations Security Council has called a special session for Thursday morning to discuss the bombings and Secretary General Kofi Annan, who was to travel to Jordan Thursday, has cancelled his trip, reports CBS News Foreign Affairs Analyst Pamela Falk.
CBS News reporter Kristen Gillespie, who lives a block away from the hotels, was on the scene soon after the explosions. As bodies were being removed from the hotels, dozens of guests milled around,