Government leaders say the new legislation will provide "quick and just deterrence" against what it called "terrorism".
Egypt's chief prosecutor was killed by a car bomb explosion on Monday, while the Sinai assaults mark a significant escalation in fighting in the desert peninsula.
Fighters say they simultaneously attacked 15 military checkpoints in El Arish, Sheikh Zuweid and Rafah.
The Muslim Brotherhood, which the Egyptian government considers a terrorist organisation, is calling on supporters to "rise in revolt", after accusing police of killing 13 of its members.
A statement by the group said: "To the proud people of Egypt… This unjust tyrant has done his worst. Rise in revolt to defend your homeland, your lives and your children ... Oust the heinous murderer."
Is Egypt on the offensive, and the defensive?
Presenter: Adrian Finighan
Guests:
Omar Ashour - senior lecturer of security studies at the University of Exeter
Marwa Maziad - fellow at the Middle Center at the University of Washington, focusing on civil-military relations
Daniel Nisman - chief executive of the Levantine Group, a geopolitical risk and research consultancy
Source: Al Jazeera
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