The warning came after an Egyptian truce initiative failed to halt militant rocket attacks on Israel.
Hamas initially rejected the truce but an official later told the BBC it would consider a political solution.
Palestinian officials say Israeli raids have killed 204 people so far. Israel on Tuesday reported its first fatality.
Ten people were reported killed in Gaza in overnight attacks.
The resumption of air strikes comes after Israeli Prime Minister Benjamin Netanyahu said he had “no choice” but to step up the military campaign.
“When there is no ceasefire, our answer is fire,” Mr Netanyahu said.
The Israel Defense Forces (IDF) are using recorded telephone messages, warning 100,000 residents of Gaza to leave their homes before 08:00 (05:00 GMT) on Wednesday.
Israel also targeted the house of a senior Hamas official in western Gaza early on Wednesday.
Mahmud al-Zahar, a member of the political bureau of the movement, was not at home at the time.
Israel launched its Operation Protective Edge eight days ago. Its stated objective is to halt Palestinian rocket attacks on Israel, but the UN says the majority of those killed in Gaza have been civilians.
Hamas says the terms of the ceasefire did not address concerns over the economic blockade of the Gaza strip, which has caused severe economic hardship for many Palestinians.
PM ‘a failure’ The Egyptian-backed truce was to have started at 09:00 (06:00 GMT) on Tuesday.
Israel’s security cabinet approved it and operations were halted for six hours.
However, Israel then resumed its attacks on Gaza, saying militants had continued to fire dozens of rockets.

 Mr Netanyahu said: “This would have been better resolved diplomatically, that’s what we tried to do when we accepted the Egyptian truce proposal.
“But Hamas leaves us no choice but to expand and intensify the campaign against it.”
One senior Hamas spokesman, Osama Hamdan, told the BBC it had only heard about the truce initiative through the media and that a ceasefire could not be put in place without the details of any agreement being known.

The armed wing of Hamas, the Izz al-Din Qassam Brigades, dismissed the initiative, saying its battle with Israel would “increase in ferocity and intensity”.
Under the terms of the Egyptian initiative, the ceasefire should have been followed by a series of meetings in Cairo with high-level delegations from the two sides.

Moussa Abu Marzouk, a top Hamas official, said no final decision had been taken on the Egyptian initiative.
But he told Lebanese TV: “The siege on Gaza must be broken and the people of Gaza should live freely like other people of the world.”
Another Hamas leader in Gaza, Mushir al-Masri, told Associated Press that mediators and international guarantees would be needed for any deal to work.
Mr Netanyahu had come under fire in Israel for accepting the truce initiative.
His office announced that deputy defence minister Danny Danon had been sacked for comments branding the PM a “failure”