"About four or five explosions were heard in and around Eilat -- it seems they were caused by rockets," police spokesman Mickey Rosenfeld told AFP.
"We are still searching to find the rockets," he said, saying that no one had been hurt in the attack.
Eilat police chief Moshe Cohen said one or two of the rockets had apparently landed in Jordan while another two landed in the sea.
"Apparently one or two landed in Jordanian territory, and another two landed in the water," he said, without saying where the fifth had landed.
A police investigation was under way but initial reports suggested the rockets had been fired from the south, Cohen said.
In Amman, Jordan's Interior Minister Nayef Qadai told AFP that two cars were wrecked in the rocket blast, which occurred near a hotel.
"A Grad rocket fell in the street in Aqaba, near to the Intercontinental hotel, destroying two cars and injuring four people, one of them seriously," Qadai said.
Information Minister Ali Ayed said in a radio interview the blast occurred at around 7:45 am (0445 GMT).
Eilat, a coastal resort located at Israel's southernmost point, lies several kilometres west of the border with Jordan, and a similar distance from the border with the Egyptian Sinai.
The Israeli military said it was investigating the source of the fire and was in constant contact with the authorities in Egypt and Jordan.
"The IDF (Israel Defence Forces) and Israel police are searching the area and examining the source of the firing," a spokeswoman said. "The IDF maintains ongoing contacts with the Jordanian and the Egyptian authorities."
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