The officials said the near-simultaneous attacks today took place at and around the town of Sheikh Zweid and left 11 soldiers wounded. They said the death toll is likely to rise.
The officials spoke on condition of anonymity because they were not authorized to speak to the media.
Egyptian security forces have for years battled militants in northern Sinai, which borders the Gaza Strip and Israel.
But the insurgency there has gained momentum after the Egyptian military ousted an elected Islamist president in 2013.