Airstrikes and rocket attacks between Israeli and Palestinian fighters killed several people on Saturday.
Following the border violence, Egyptian officials tried to secure a tacit truce between the two sides.
But the attempt failed on Sunday as Israel said that three rockets had been fired at them from Gaza after the ceasefire deadline had passed.
Saturday's exchange began with an Israeli attack in Rafah city, which Israel said was in response to rocket attacks launched from Gaza earlier in the week.
Al Jazeera's Julia Mills reports.