"We are building a fence. It can't stop missiles but we will find a solution for that. We will strike those who aim to harm us," he said Thursday.
Wednesday night saw terrorists fire three rockets at Israel's southern resort city.
One Grad rocket exploded in a construction site in a residential area in the city. No injuries or damage were reported.
Security forces are still canvassing the city for the remnants of the other two rockets.
Defense Minister Ehud Barak, IDF Chief of Staff Lt-Gen Benny Gantz, GOC Southern Command Maj-Gen Tal Russo and Military Intelligence Chief Maj-Gen Aviv Kochavi held a security assessment following the rocket fire on Eilat.
The IDF has been on high alert across the Israel-Egypt border following several attempts to mount terror attacks in the sector.
So far, the police and Home Front Command have not issued any special security directives for the area's residents.
"The situation in Sinai requires a different kind of deployment," he said. "This was a serious incident. We're studying it and we will go after those who fired on Eilat and targeted Israeli citizens."
Meanwhile, Egyptian media quoted Mahamoud El-Hefnawy, Cairo's director of security for the Sinai sector, as saying that Wednesday's rocket fire did not emanate from Sinai.
Hefnawy said that "the situation in the southern sector is excellent. There are regular patrols and stakeouts across all roads. If anyone seems suspect they are stopped for inspections meant to stop any terrorist elements from entering the area." He added that Egyptian border patrols are constantly present across the sector.
Also on Thursday, United States Ambassador to Israel Dan Shapiro visited one of the Iron Dome batteries stationed in southern Israel.
Commenting on the rocket attack on Eilat he said that there was a serious threat to Israel and its citizens from Gaza and from Sinai.
The US, he said, will always support Israel's right and ability to defend itself. Shapiro noted that Iron Dome's operational success has prompted the American president to ask Congress to approve additional funding for more batteries.
Ahuva Mamos, Roi Kais and Yoav Zitun contributed to this report
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