“Eilat and other Jewish cities will not enjoy security, tourism or economy, and Jews will pay a high price for the blood of the Mujahideen," the Mujahideen Shura Council group said in a statement on Tuesday.
According to the Jerusalem Post, Israel's Iron Dome missile system intercepted the rocket.
Another group, called Ansar Bayt al-Maqdis, said that five of its members were killed in an Israeli drone attack in Egypt's restive Sinai region on Friday.
However, Egyptian security sources said the four had been killed by an Egyptian helicopter as they were setting up a rocket launch pad.
Militants have stepped up attacks, mainly targeting security forces in Sinai, since the army's overthrow of president Mohammed Morsi on July 3.
Sinai has been largely demilitarized, in line with the 1979 peace treaty between Egypt and the Israel regime.
BA/BA