With unrest sweeping the country, Egypt is believed to have moved several dozen armored vehicles to the volatile border area to contain militant activity. The Israeli military gave no details.
Under a 1979 peace treaty, Egypt is required to coordinate any special military activity in the area with Israel.
In a statement Tuesday, the Israeli army said "the Egyptian military activity in Sinai is coordinated with Israeli security elements and authorized at the most senior levels in Israel, to contend with security threats in Sinai that pose a threat to both Israel and Egypt."
Violent Islamic extremists are gaining strength in Sinai, and Palestinian militants have infiltrated through tunnels from Gaza.
Earlier on Tuesday, images from Al Jazeera's Egypt news channel satellite showed troops chanting, marching and training for unarmed combat in the streets of the Red Sea city of Suez.
A day earlier, as the armed forces issued an ultimatum to the Islamist president Mohammed Morsi and his opponents to resolve a political deadlock, rival factions exchanged fire in the city, witnesses said.
Security sources in Suez said that forces from the locally based Third Field Army strengthened their presence in the city overnight after the clashes. Armed vehicles were also sent on patrol, the sources told Reuters.
Egyptian officials have said security on the Suez Canal, the vital world waterway, had not been affected by unrest. Cities on the canal have seen major anti-government protests during and since the revolution of 2011.
Military sources said on Tuesday that troops were preparing to deploy on the streets of Cairo and other cities if necessary to prevent clashes between rival political factions
The political wing of the ruling Muslim Brotherhood has called on supporters to take to the streets to resist an army move that a spokesman compared to the coup which brought Egypt six decades of military-backed rule.
"This is a very critical moment in Egyptian history - we are facing a moment very similar to 1952," Freedom and Justice Party spokesman Murad Ali told Reuters on Tuesday. In that year, Gamal Abdel Nasser and the Free Officers overthrew King Farouk.
"Egyptians are very aware that there are some people that are trying to push the country back in history and back to dictatorship."
The head of Egypt's armed forces announced on Monday that the army was giving politicians 48 hours to answer demands made by the Egyptian people or the military would offer its own "road map for the future."
"The people agreed to a constitution and this constitution draws the map," Ali said. "We are refusing any attempts at a coup or any attempts to overlook the constitution that Egyptians agreed upon."
The Freedom and Justice Party is part of the alliance of Islamist parties calling on Egyptians to "go and defend their democracy and their right for freedom", Ali said, adding that he expected people to turn out in large numbers across the country."
The alliance said late on Monday that it rejected attempts by some to use the army to "assault legitimacy" in a partisan way that would lead to a coup.
The Brotherhood said on Monday that it was considering action to defend itself after its national headquarters were ransacked.
Since then, other senior members have called for action. "Preventing this coup may call for martyrdom, which we would offer as a mark of loyalty to the martyrs of the revolution," Mohamed El-Beltagi said in comments on the FJP website, referring to those who died in the 2011 uprising.
Ali said that his group was not handling the logistics of organizing these rallies, but said that Egyptians were taking to the streets of their own accord "refusing the intervention of the military in political issues."
The Brotherhood's Misr 25 television channel broadcast images late on Monday of large gatherings in a number of Egyptian cities. Brotherhood spokesman Gehad El-Haddad tweeted that there were 50 "pro-legitimacy" demonstrations happening across Egypt's 27 provinces.
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