Israeli strikes killed at least 34 people in the Gaza Strip on Wednesday, including 26 in Gaza City alone, the Palestinian news agency WAFA reported.
Israel has said it plans to take full control of the strip's largest city, where around one million people - roughly half of the territory's population - were still believed to be sheltering.
Israeli Prime Minister Benjamin Netanyahu said on Sunday that about 100,000 Palestinians had so far left the city. Aid groups warn the offensive will worsen an already catastrophic humanitarian situation.
The Israeli military said it struck a high-rise building in Gaza City that was being used by Hamas. Residents had been warned beforehand, according to the army. The claims cannot be independently verified.
For the first time on Tuesday, Israel's military called on all Gaza City residents to evacuate.
Troops have sent voice and text messages and dropped leaflets urging civilians to leave, warning: "Staying in this area is very dangerous."
Meanwhile, EU chief Ursula von der Leyen said on Wednesday she would push to sanction "extremist" Israeli ministers and curb trade ties over Gaza, as she warned famine could not be used as a "weapon of war".
Addressing the European Parliament, Von der Leyen lamented that divisions among member states were holding back a European response and said the European Commission she leads "will do all that it can on its own".
"What is happening in Gaza has shaken the conscience of the world. People are killed while begging for food. Mothers holding lifeless babies. These images are simply catastrophic," Von der Leyen said.
"For the sake of the children, for the sake of humanity - this must stop."
The German politician said the commission would put its bilateral support to Israel on hold, stopping all payments, but without affecting work with civil society groups.
The measure is to affect future allocations amounting to about six million euros ($7 million) a year and the disbursement of about 14 million euros for ongoing institutional cooperation projects, the commission said.
The European Union's executive will propose sanctions on "extremist ministers" - whose actions and words "incite violence" - and "violent settlers".
And it will push for a partial suspension of an association agreement with Israel on trade-related matters.
But such measures will need approval by the bloc's 27 member states, which have been deeply divided on how to respond to Israel's actions in Gaza.
"I am aware it will be difficult to find majorities," Von der Leyen conceded.
"And I know that any action will be too much for some. Too little for others. But we must all take our own responsibilities".
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