Two men on a motorcycle gun down parliamentary-hopeful Mostafa Abdelrahman of the Salafist Nour party in al-Arish.
At least nine people including four Egyptian policemen were killed when a suicide bomber rammed his vehicle into a police club in the Sinai Peninsula, state media reported.
State television said several people were also wounded in the bombing on Wednesday in North Sinai provincial capital el-Arish.
Later on Wednesday, sources told Al Jazeera that a further three people including a child were killed by a warplane missile south of Sheikh Zuwied, in North Sinai governorate, which is some 40km away from the first attack.
Sinai Province, the local affiliate of the Islamic State of Iraq and the Levant (ISIL), claimed responsibility for the first attack, which it described as a suicide bombing.
The rebel group has carried out a string of attacks – killing hundreds of soldiers and police since the army toppled former President Mohamed Morsi in 2013 – in or around the provincial capital in recent months.
The attacks came after the army launched a sweeping campaign in the peninsula bordering Israel and the Gaza Strip.
Wednesday’s attacks came days after a Russian passenger plane crashed in the peninsula after taking off from a resort airport in South Sinai, killing all 224 people on board.