The statement said the bombings targeted the US business community and "infidels who fight Islam and Muslims".
The statement said the bombings were "done by a holy warrior brother against the American Chamber of Commerce and Industry".
Among the victims of the Marriott explosion were more than a dozen prominent business executives from Western corporations, who were attending a weekly breakfast in the lounge.
|Fugitive Noordin Mohammed Top is said to have claimed responsibility for the hotel blasts
The attack also killed a New Zealander, three Australians and an Indonesian cook. At least six Americans were wounded.
The statement said the blast at the Ritz-Carlton hotel was aimed at football players from Manchester United, although they had not been due to check in until the following day.
The team cancelled its visit to Indonesia in the wake of the attack.
"Those players are God's enemies who do not deserve honors and respects from Muslims," said the note, which was signed by the "leader of the Tandzim al-Qaeda Indonesia'' and included Noordin's full name.
The group's name reinforces previous intelligence claims that JI has links to the al-Qaeda network.
Police said they were investigating the message, but were not sure if it was truly from Noordin or if it will provide new clues in the hunt for those responsible for the blasts.
Written in Arabic and Indonesian, the message was posted on a previously unknown website on Sunday.
Noordin is accused of planning four previous attacks in Indonesia that killed more than 240 people.
His group claimed responsibility for one of those attacks - triple suicide bombings in Bali in 2005 - in a similar note.
"It is entirely plausible that the statement could have originated from Noordin Top, but we can't really know for sure," Jim Della-Giacoma, Southeast Asia project director for the International Crisis Group, told the Associated Press.
"It is interesting that the statement mentions the names of two late close associates of Noordin, both of whom were killed by police."
The statement said the twin bombings were carried out in honour of Azahari bin Husin, a JI bomb maker who was shot dead by security forces in 2005, and Sariyah Jabir, another explosives expert who was killed in 2006 during a raid on a JI hide-out in central Java.
The men are believed to have played crucial roles in the Bali bombings in 2002 and 2005, a previous attack on the Marriott in 2003 and a truck bombing at the Australian Embassy in 2004.