They said the mother of the two siblings was killed last week by militants from the Islamic State group when they raided the family home in the village of Yamit, west of Rafah, and kidnapped the three men they suspect of being collaborators.
The three decapitated bodies found today were taken to hospital, where they were identified and prepared for burial, according to the officials and witnesses, who spoke on condition of anonymity because they were not authorised to speak to the media and feared reprisals, respectively.
Islamic militants have been fighting security forces in northern Sinai for years, but the insurgency has grown deadlier and expanded since the military's 2013 ouster of an Islamist president Mohammed Morsi of the now-outlawed Muslim Brotherhood whose one year in office proved divisive.
Lately, the militants have targeted Egypt's minority Christians, forcing hundreds of them to flee their homes in northern Sinai after killing several of them there.
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An IS leader in Egypt vowed this week to escalate attacks against Christians, urging Muslims to steer clear of Christian gatherings and western embassies as they are targets of their group's militants.
"Targeting the churches is part of our war on infidels," the unidentified leader said in a lengthy interview published by the group's al-Nabaa newsletter on Thursday.
He said churches, security posts and institutions, as well as places where "crusader nationals of western countries" gather were all "legitimate targets."