Egypt said the group was traveling without formal authorization in the western desert near Libya, where security forces are battling Islamic militant groups.
A militant group based in the Sinai that has sworn allegiance to the Islamic State said the attack was retaliation for Egypt's execution of six of its members.
President Abdel Fattah al-Sisi, who initially took power after a 2013 coup, said the new laws were needed to combat insurgents, including the banned Muslim Brotherhood. Rights groups say the legal definitions of terrorism are too broad.
Terrorism is nothing new in the Sinai. But it has evolved in a more dangerous direction for Egypt, and President Sisi's tactics don't seem to be working.
A wave of repression by the Sisi regime the past two years has been matched by a rise in Islamist attacks. Following the car bomb in Cairo Monday, both sides are likely to up the ante.
Egypt's tourism has taken a beating in recent years, and the attack at Luxor's Karnak temple complex, one of its most famous archeological sites, won't help.
After years of revolt and turmoil, Egypt is in a period of historic oppression. And world powers like the United States are pretty much OK with that.
An Egyptian court sentenced the former president to death last month. The court's now waiting on the country's top cleric to make a recommendation in the case.
Western powers are concerned that the fractured nation in North Africa is fertile ground for Islamic State militants.
Egypt's airstrikes came in response to the mass beheadings of 21 Egyptian Christians by IS militants in Libya. The Libyan government has called for the US-led coalition in Syria and Iraq to turn its attentions to Libya.
Two Al Jazeera English journalists have posted bail, and the government of President Abdel Fatah al-Sisi has hinted at a pardon. But the press environment is largely hostile.