Dozens of people have been arrested in Jordan following the suicide bombings that killed at least 57 people and wounded nearly 100 in the capital.
Jordanians are angry a wedding was hit in the bombings
The arrests came as al-Qaeda in Iraq allegedly named the four bombers - all Iraqis, including a husband and wife.
"They vowed to die and they chose the shortest route to receive the blessings of God," the statement said.
In Amman, UN Secretary General Kofi Annan condemned the "heinous crime" and "the scourge of terrorism".
"No ideology, no cause can justify the vicious killing of innocent civilians," said Mr Annan.
The al-Qaeda statement appeared on a website often used to make such claims, but it has not been independently confirmed.
It named the bombers as Abu Khabib, Abu Muaz, Abu Omaira and Om Omaira.
It said the hotels that had been bombed were centres for launching wars on Islam.
The group seems to have been taken aback by the furious response, which included marches in Amman calling for its leader to "burn in hell".
The BBC's Jon Leyne in Amman says it is unusual for the group to put out additional statements justifying its actions.
Many Jordanians have - or had - some sympathy for the group, but few understand the reason for bombing a wedding.
King Abdullah vowed Jordan was "not afraid" and would not be cowed into changing its policies.
Most of the casualties in Wednesday's attacks were Jordanian.
The Grand Hyatt, Days Inn and Radisson SAS hotels were the targets of the bombings. The blast at the latter caused carnage at a wedding reception.
Prayers and condemnation
Jordanians have been saying special prayers of mourning in mosques and taking part in rallies on Friday.
There has been condemnation of the bombings from Arab voices ranging from Saudi newspapers to Palestinian militants.
A Hollywood producer and his daughter were killed in the blasts
Syrian-born Hollywood producer Moustafa Akkad - who was behind the Halloween horror films and the Anthony Quinn epic The Message - died on Friday of wounds sustained in the bombing.
His 33-year-old daughter Rima was killed in the blast.
The producer's death took the number killed to 57. At least three bombers also died.
DNA tests are being used to identify at least 14 bodies, including those of the bombers.
Jordan has become a base for Westerners who fly in and out of Iraq for work and has long been regarded as a prime target for attack, correspondents say.
Security has been tightened around Amman and Jordan's land borders have been closed.
1. Vehicle explodes outside hotel after being stopped at a police checkpoint
2. In the most deadly attack, a bomb destroys a banquet room where a wedding reception was being held. Dozens injured by shrapnel
3. Suicide attacker detonates bomb in hotel bar, just before 2100 local time. Two senior Palestinian officials are among the dead