The ground operation was preceded by several hours of heavy artillery fire after nightfall.
Israeli airstrikes also intensified just as the ground operation was getting under way, killing 28 Palestinians.
Defense Minister Ehud Barak says the aim of the ground push is to protect Israel from Hamas' rocket attacks.
Ehud Barak, Israeli Defense Minister, said, "It will not be easy or short but we are determined. We have no aggressive intentions though. We hope the situation will remain calm. Nevertheless, we are ready and alert to face any unwanted development in that area. We are peace-seekers. We have restrained ourselves for a long time, but now is the time to do what needs to be done."
Hamas leaders have warned that a violent welcome is in store for the Israeli soldiers.
They've also threatened to resume suicide attacks inside Israel.
In addition, Hamas says it had broadcast a message on Israeli military radio frequencies, promising to kill and kidnap the invading soldiers.
(CCTV January 4, 2009)