The official spoke Tuesday after Israeli Cabinet ministers discussed a spike in rocket fire from Gaza.
He said ministers approved military operations ranging from surgical strikes on Palestinian militants to a broad ground offensive.
He was talking on condition of anonymity due to the sensitivity of the issue.
The decision stopped short of ordering a ground assault. Rocket fire has all but stopped over the past day.
Egyptian officials said Israel agreed to put off wider operations in Gaza to give Egypt time to get Palestinian militants to stop rocket fire.
Violence flared when Gaza militants pounded southern Israel with rockets and Israel hit back with airstrikes.