An Internet statement, which could not be immediately verified, said militants from the group carried out the attacks.
Among those killed were two high-ranking Palestinian security officials, according to the Palestinian envoy to Amman.
Jordan's deputy Prime Minister Marwan Moasher earlier said Iraq-based militant Abu Musal al-Zarqawi is a leading suspect, and security sources have also pointed the finger at al-Qaeda.
The internet statement said al-Zarqawi, who leads Iraq's al-Qaeda, would later give more details on the attack.
The near simultaneous blasts occurred at the Radisson SAS, the Grand Hyatt and the Days Inn in the commercial Jebel Amman district of the city, frequented by foreign business people and diplomats.
The first, and deadliest, blast hit the five-star Radisson SAS at 9:02 pm local time in a ballroom where a wedding reception was underway.
"We thought it was fireworks for the wedding but I saw people falling to the ground," said Radisson wedding guest Ahmed.
"I saw blood. There were people killed. It was ugly."
It was immediately followed by a second blast at the entrance of the Grand Hyatt, about one kilometre away.
A third blast occurred at the Days Inn hotel, a three-star establishment in Rabiyeh neighbourhood where the Israeli embassy is located.
Jordanian Prime Minister Adnan Badran rushed to the Grand Hyatt, news agency AFP reported, while police threw barricades around the area.
Jordan's King Abdullah blamed a "deviant and misled group" for the attacks.
The prime minister later ordered schools and government offices closed and sealed borders.
"All our land borders have been closed for an indefinite period of time but airspace has not been closed although security has been reinforced at the airports," Deputy Prime Minister Moasher said.
A BBC reporter was in the Grand Hyatt at the time of the blasts and described a huge explosion which caused windows to be blown out, followed by panic and chaos as survivors tried to flee the hotel.
Police and medics evacuated the buildings and the injured were taken to hospitals.
Jordanian-born Zarqawi has been condemned to death in absentia in Jordan for the 2002 murder of a diplomat in Amman.
Earlier, Mr Moasher told AFP that two of the bombings appear to have been caused by bombers with suicide belts, while a third was likely a suicide car bomb.
The largest number of casualties was suffered at the Radisson, he said.
"It looks so far as if most of (the victims) are Jordanians," he also said in comments broadcast by CNN.
The other suicide bomber targeted the Grand Hyatt, while a car bomber attempted to cross a security barrier outside the Days Inn, which is near the Israeli embassy in Jordan.
The Jordanian authorities have in the past broken up a number of al-Qaeda-linked networks suspected of plotting attacks against US and other Western targets in Jordan.
Attacks condemned
Cutting short an official visit to Kazakhstan to return home, Jordan's King Abdullah II condemned the attacks as "criminal acts committed by a deviant and misleading bunch" and said they would not sway Jordan from continuing its battle against terrorism.
"The hand of justice will get to the criminals who targeted innocent secure civilians with their cowardly acts," he said in a statement carried by the official Petra news agency.
Messages of commisseration have poured in from around the world, and the United Nations Secretary-General Kofi Annan cancelled plans to visit Amman on Thursday.
United Nations Secretary General chief Kofi Annan, currently visiting Saudi Arabia, postponed a scheduled trip to Jordan this week in light of the attacks, his spokesman said.
Jordan, a close US ally in the Middle East, has until now been known as one of the most stable nations in the region and the hotel attacks appeared to be the first militant strike of its kind against the kingdom.