The assailants attacked the security guards at Farafra checkpoint in Wadi al-Jadid governorate, which borders both Sudan and Libya, on Saturday.
Security officials had said the assailants were smugglers.
But an army spokesman had said on his Facebook page that "terrorists" -- the term authorities use to describe Islamist militants -- were behind the attack.
Two smugglers were also killed in clashes with the guards.
"I swear that we won't leave them and we will take revenge," said Sisi during his speech last night on the occasion of Layla Al-Qadr (the night of revelation).
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Laylat Al-Qadr, considered the holiest night of the year for Muslims, is traditionally celebrated on the 27th day of Ramadan.
Sisi has repeatedly expressed concerns about militants who have capitalised on the chaos in Libya and set up operations along the border.
In his speech, the president said the teachings of Quran should be applied in daily life. He said the extremists offend the religion by killing innocent people.
"We should apply the teachings of the Quran and understand it," he said during the televised speech. "We have to be a good example for Islam."