The statement, which could not be authenticated, was signed by the Abdullah al-Azzam Brigades of al-Qaida Organisation in the Levant and Egypt.
Three rockets fired at two US Navy ships in Jordan's Aqaba port on Friday, missed their targets and hit a warehouse and a hospital, killing a Jordanian soldier, as well as the Israeli port of Eilat.
The attackers fired a rocket near the USS Ashland, but the missile missed the vessel and hit a nearby warehouse and a hospital instead, US military officials said.
Jordanian soldier Ahmad Jamal Salih was fatally wounded, and another soldier injured, when a mortar sailed over a US Navy ship docked in Aqaba and hit a warehouse, a Jordanian military source said.
The devices were believed to have been Katyusha rockets fired from a poor neighbourhood on the outskirts of Aqaba, a Jordanian Red Sea port 350km south of the capital Amman.
Immediately after the attack, the two US amphibious assault ships, which had been on a joint training exercise with the Jordanian navy, weighed anchor and headed for the safety of open waters.
The two US naval ships left the
port after the attack
Earlier Israeli police and witnesses said a Katyusha rocket fired from Jordan fell on the outskirts of the nearby airport of Israel's Red Sea resort of Eilat, but did not explode.
The claim for Friday's attack was carried on a website not often used by other groups which say they are linked to Osama bin Ladin's network.
"A group of our mujahideen have targeted US vessels in Jordan and (Israel's) Eilat port with three Katyusha rockets before safely returning to their base," the statement said.
"Zionists are a legitimate target and we warn the Americans, who are spreading their corruption throughout the world and who have stolen the wealth of the Muslim nation, to expect even more stinging attacks.
"This is our debut operation in Jordan," it added. "And as we have begun to destroy the throne of the Egyptian tyrant, we warn the Jordanian tyrant to release our jailed brothers and voluntarily abdicate before we force you to go."
A Jordanian security source said authorities were searching
for three men in the Katyusha missile attack, which was launched from an industrial warehouse area near the entrance to the city.
"We are searching for a Syrian and two Iraqis who are in
"We are searching
for a Syrian and two Iraqis who are in Aqaba and used Kuwaiti
Jordanian security source
Aqaba and used Kuwaiti number plates," the source said.
Aqaba and Eilat are about 15km apart and located on either side of the Jordan-Israeli border at the northern end of the Red Sea, close to Sinai Peninsula.
The attacks come amid a time of tension in the region marked by Israel's withdrawal from the occupied Palestinian territory of Gaza.
Jordan, which is also home to 1.8 million Palestinian refugees and their descendants, and Israel signed a 1994 peace deal.
Israeli Defence Minister Shaul Mofaz, speaking in southern Israel, said three missiles landed in the city of Eilat itself, near its airport and also in Aqaba, adding the attacks were "intended to hit the Israeli side and the Jordanian side as well".
"We still don't know who is behind this act but I'm sure the Jordanians will do all they can to prevent such attacks in the future as in the past," Mofaz said, adding that Israeli authorities are in contact with Jordanians over the incidents.
The US Navy's 5th Fleet based in Bahrain confirmed that a mortar was fired from Jordan at one of its ships docked in the seaport of Aqaba, missing the vessel but hitting a warehouse on a dock.
"At approximately 8.44am local time a suspected mortar rocket flew over the (amphibious) USS Ashland over the bow and impacted a warehouse on the pier in the vicinity of the Ashland and the USS Kearsarge which were in port," Lieutenant Commander Charlie Brown said.
"The warehouse sustained an approximate 2.5 metre hole in the roof of the building and no sailors or Marines were injured in the attack," Brown said, adding that the missile was fired from land.
Mofaz said the attackers
targeted Israel and Jordan
One missile narrowly missed the USS Ashland, an amphibious warfare ship that is designed to transport Marines and to launch assault landing craft and helicopters.
"I can confirm that a rocket flew over the bow of USS Ashland and the rocket impacted in the roof of a warehouse. No sailors or Marines were injured," Commander Jeff Breslau of the US Fifth Fleet in Bahrain.
"It's pretty safe to conclude that they were probably trying to hit one or both of the ships," he said.
The rocket fired into Israel created a small crater in the road, about 15 metres from the Eilat airport fence, said a local police commander, Avi Azulin.