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Finance Minister Yuval Steinitz said just one hacking attempt was successful on a site he did not want to name, but it was up and running after 10 minutes of downtime.
Typically, there are a few hundred hacking attempts a day on Israeli sites, the ministry said.
Attempts on defence-related sites have been the highest, while 10 million attempts have been made on the site of Israel's president, 7 million on the Foreign Ministry and 3 million on the site of the prime minister.
A ministry spokesman said while the attacks have come from around the world, most have been from Israel and the Palestinian territories.
"The ministry's computer division will continue to block the millions of cyber attacks," Steinitz said. "We are enjoying the fruits of our investment in recent years in developing computerised defence systems."
Steinitz has instructed his ministry to operate in emergency mode to counter attempts to undermine government sites.
Both sides in the Gaza conflict, but particularly Israel, are embracing the social media as one of their tools of warfare. The Israeli Defense Force has established a presence on nearly every platform available while Palestinian militants are active on Twitter.
"The war is taking place on three fronts. The first is physical, the second is on the world of social networks and the third is cyber," said Carmela Avner, Israel's chief information officer.
Last month, U.S. Defence Secretary Leon Panetta said cyberspace is the battlefield of the future, with attackers already going after banks and other financial systems. U.S. banks have been under sustained attack by suspected Iranian hackers thought to be responding to economic sanctions aimed at forcing Tehran to negotiate over its nuclear programme.