"Egypt will never, under any circumstances, tolerate the use of its lands by any party to harm the country's interests," the agency quoted the source as saying in an apparent admission that the rockets had been fired from Egypt.
Sami Abu Zuhri, a spoksman for Hamas, the Palestinian group that runs the Gaza Strip, said the allegations were "silly".
"Egyptian statements are conflicting," Abu Zuhri said. "We doubt the credibility of these statements and believe they are unprofessional and politically motivated."
Hamas have also been accused by Israel of carrying out the strike, but have denied any involvement.
"We doubt the credibility of these statements and believe they are unprofessional and politically motivated"
Sami Abu Zuhri, a spokesman for Hamas
The MENA report comes a day after Egypt lauched a security operation on the Sinai peninsula in response to Jordanian claims that they had proof the rockets that hit Aqaba, killing a taxi driver, were fired from the desert region.
"Following the Jordanian comments, Egypt has launched a wide security sweep of the Sinai peninsula," an Egyptian official said on condition of anonymity because he was not authorised to speak to the media.
But he insisted "there are no organised groups operating in Sinai and security on the peninsula is extremely tight. Any suspicious activity would have been detected," he said.
South Sinai Governor Abdel Fadil Shusha said it was "technically impossible" for attacks to have been launched in the Sinai due to the mountainous nature of the terrain.
The Egyptian government has yet to officially comment on the rocket attacks, which were swiftly condemned by the United States and Russia.
On Monday, Israeli police said reports suggested the rockets had been fired from "the south," an apparent reference to the Sinai peninsula, which lies some 10km south of Eilat.
A similar rocket attack hit Aqaba and Eilat in April, although the source of the firing was never established. Another attack on the Red Sea ports in 2005 was claimed by an armed group operating from Sinai.