The warnings were sent by text messages and automated phone calls, as well as leaflets dropped from the air reading, "The I.D.F. (Israel Defense Forces) does not want to harm you, and your families. Whoever disregards these instructions and fails to evacuate immediately endangers their own lives, as well as those of their families."
The I.D.F. said it struck 39 targets overnight.
Homes were bombed of prominent leaders of Hamas -- the militant group overseeing Gaza -- as was the new Interior Ministry building, according to witnesses.
The assault came after Hamas and other militant groups ignored a six-hour cease-fire Tuesday, which Egypt had brokered. Over 125 rockets were fired from positions in Gaza into Israel, none doing significant damage, Tuesday.
Aerial fire by Israel into Gaza, by contrast, were planned and accurate. Military spokesman Lt. Col. Peter Lerner said Hamas leaders' homes were chosen as targets because "They are key players in the decision-making of Hamas's terrorist machine."
The Palestinian Health Ministry reported 201 deaths in Gaza in the nine-day conflict; Israel has reported only one death -- that of a civilian, killed by mortar fire near the Gaza-Israel border.
The activist group Human Rights Watch, quoting United Nations figures, said in a report Wednesday that 1,255 homes in Gaza had been destroyed, leaving about 7,500 people refugees.
"Israel's rhetoric is all about precision attacks, but attacks with no military target and many civilian deaths can hardly be considered precise. Recent documented cases in Gaza sadly fit Israel's long record of unlawful airstrikes with high civilian casualties," said Sarah Leah Whitson, Middle East Director of the organization, in the report.
While Israel has massed troops on the border for a possible ground invasion, the engagements thus far have been entirely through the air, with Israel's anti-missile defense system the Iron Dome effectively intercepting Hamas missiles and rockets. Four missiles were stopped over the Tel Aviv area Wednesday.
"I call for securing the safety of the citizens of Israel. To the best of my understanding, it is not possible to ensure summer vacation, a normal summer for our kids without a ground operation in Gaza. We don't need to rule Gaza, or build settlements in Gaza. We need to ensure that all Hamas terrorists run away, are imprisoned or will die," Israeli Foreign Minister Avigdor Lieberman told Israeli radio.