The officials, who spoke on condition of anonymity because they were not authorised to brief the media, say the first attack took place in the town of el-Arish when militants opened fire on an off-duty policeman.
They said three conscripts in an armored vehicle were killed later in a roadside bomb explosion in the border town of Rafah.
Egypt has in recent years been battling a stepped-up insurgency in northern Sinai, mainly by militants from an Islamic State group affiliate.
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