Jordan has said the group led by Abu Musab al-Zarqawi is linked to rocket attacks targeting US warships in the Red Sea port of Aqaba last Friday.
Jordanian security forces have been on alert since the attacks
Zarqawi is believed to be the leader of one of the most violent insurgent groups in Iraq, and is alleged to have links with Osama Bin Laden's al-Qaeda.
In the attacks, one rocket narrowly missed a US warship, another hit a hospital and a third landed in Israel.
On Tuesday, Jordan arrested a man alleged to have planned the attacks.
A televised statement named Mohammed Hassan Abdullah Sihly, a Syrian, as prime suspect for the attacks.
Three others accused of involvement in an Iraq-based terror group fled into Iraq on Friday, the statement said.
Zarqawi's group, the al-Qaeda Organisation in the Land of Two Rivers, said it was behind the rocket attack in an internet statement on Tuesday. Zarqawi is a Jordanian national.
Interior Minister Awni Yervas said: "The investigation revealed that the terrorist group that led the Aqaba attack is linked to the al-Qaeda branch of the terrorist Abu Musab al-Zarqawi."
Jordanian officials said that the three men in custody along with Mohammed Shihy were his two sons and an Iraqi, all travelling on false Iraqi passports.
Officials said their case would be brought to court soon.
Investigators believe that the Katyusha rockets used in the attacks were smuggled into Jordan hidden in the fuel tank of a Mercedes car.
Three Katyusha ground-to-air rockets were fired from an industrial area of Aqaba on Friday.
One narrowly missed the USS Ashland warship moored close to the port city, but killed a Jordanian soldier.
The second rocket also passed close to the warship, but landed near a military hospital.
The third crossed the nearby international border and landed near an airport close to the Israeli city of Eilat.