In a dramatic turn of events, the five gunmen involved in the attack were reported killed hours later near the Israeli border, an Israeli army spokesman said.
"The bodies of the five gunmen have been found by the Israeli army," the spokesman said without giving any details.
Earlier Egyptian security sources said the five gunmen dressed up in Bedouin attire drove up to a border checkpoint between Egypt and the West Bank and opened indiscriminate fire, killing 16 border guards.
The official MENA news agency described the attackers as 'jihadists' from the Hamas-controlled Gaza strip.
Eyewitnesses said the attack came as the soldiers at the checkpoint were breaking their Ramadan fast. They said the soldiers were caught totally off guard and had no chance to retaliate.
President Mursi held an emergency meeting with military and intelligence officials and later in a televised address vowed to retake control of the Sinai.
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"The security forces will take full control of the area," Mursi said.
Hundreds of Islamists were released under a general amnesty just two weeks ago in a first major decision by the new President.
Mursi has also expressed rapprochement with Hamas hosting the premier of the deposed government in the West Bank Ismail Haniyah, exporting diesel fuel to Gaza and opening the Rafah border unconditionally.