Israel is threatening to expand its offensive unless militants release Corporal Gilad Shalit, an Israeli soldier abducted in a cross-border raid on June 25, and halt rocket fire on Israeli cities.
At least three air strikes were launched shortly after midnight local time.
One missile strike hit a suspected militant training camp in Khan Younis.
There were no reports of injuries.
At least three militants were injured in an air strike in Gaza City, Palestinian medics and police said.
Israel also bombed a key bridge in northern Gaza, despite an appeal from the United Nations to stop targeting the strip's fragile infrastructure.
The army said the goal was to prevent militants transporting rockets to launch sites.
Ismail Haniya had said the only way out of the current crisis was for all parties to restore calm through a mutual cessation of hostilities.
But officials in the Israeli Prime Minister's office said there would be no truce until the captured Israeli soldier was free.