Israeli military spokeswoman Maj Avital Leibovich said troops were continuing their advance into urban areas.
"Since the majority of the Hamas militants are pretty much in hiding in those places, mainly urban places, then we operate in those areas," she told the Associated Press.
Reservists are reported to be securing areas gained in the fighting.
Brig Gen Avi Benayahu, Israel's chief military spokesman, said thousands more - who would comprise a new, expanded phase in the ground operation if it was ordered - were still in training and had not been deployed.
Israel hopes the scale of its operation will greatly reduce the number of missiles fired from Gaza into southern Israel, while eroding support for Hamas.
Militants fired nearly 30 rockets and mortars from Gaza on Monday. One rocket struck a house in the town of Ashkelon, but no casualties were reported.
Mr Regev told the BBC that Israel's goals were "very minimalistic" and "purely defensive".
Gaza facing 'medical crisis'
"We refuse, we refuse to return to a reality in which the Israeli civilian population has to live in that constant fear of an incoming Hamas rocket," he said.
Both Hamas and Israel have rejected last week's UN Security Council resolution calling for an immediate ceasefire.
Israeli Prime Minister Ehud Olmert said "nobody should be allowed to decide for us if we are allowed to strike".
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.