"Clashes resumed between armed men and police forces in front of police station number two in al-Arish," Nile News television reported Thursday.
The army's crackdown on militant groups operating in the Sinai came three days after 16 Egyptian police and soldiers were killed by gunmen who attacked a military post on Sunday and then broke through the border into Israel to launch a separate attack there.
Egypt's Supreme Council of the Armed Forces, which relinquished official leadership of Egypt June 30 when Mohamed Morsi became president, said overnight air strikes Wednesday to rout the area of Islamist militants were carried out "successfully."
Masked gunmen had tried to shoot down the aircraft using heavy machine guns and artillery, the state-run Middle East News Agency reported.
The armed forces council, made up of senior Egyptian military officers, appealed to Sinai residents and tribes to cooperate as the military and Interior Ministry offensive sought to "restore security and stability" to the desert territory bordering Israel and the Gaza Strip, state-run Nile News reported.
While Egyptian media said at least 20 suspected militants were killed Wednesday, Sinai residents disputed that account in interviews with The Washington Post, saying the offensive appeared to have been merely a show of force and a publicity stunt.
The Sinai campaign -- marking the first time Egyptian fighter planes have carried out strikes in the region since the 1973 Arab-Israeli War -- was praised by the White House Wednesday.
Press secretary Jay Carney commended the 40-day-old government for showing "a willingness to take action when necessary."
The campaign appeared to have the blessing of Israel, The Washington Post said.
"The penny has dropped in Egypt, their level of awareness has been heightened," senior Israeli Defense Ministry official Amos Gilad told Israel's Army Radio. "They are moving to action."
No group has claimed responsibility for Sunday's attack. But Egyptian state media reported Wednesday the Army of Islam, a Gaza-based group affiliated with al-Qaida, was involved. The U.S. State Department has labeled the Gaza group a terrorist organization.