Israeli warplanes moving deeper into the residential areas have pounded the homes of Hamas leaders.
Palestinian militants still managed to fire off at least 15 rockets on Monday into the southern city of Ashkelon despite the close presence of Israeli troops.
According to Israeli prime minister, Israel would end the conflict if rocket fire on Israel stops and Hamas is unable to rearm.
At least 16 Palestinians were killed on Monday of which one was a militant.
The army announced Sunday that it was sending reserve units into Gaza to assist thousands of ground forces already in the territory.
The use of reserves is a strong signal that Israel is planning to move the offensive, which Gaza officials say has killed some 910 Palestinians, into a new, more punishing phase.
Both sides continue fighting despite international calls for a cease fire agreement.