Israeli aircraft fired missiles at the office of Palestinian Prime Minister Ismail Haniyeh of Hamas in the early hours of Sunday, setting the building on fire.
Other targets overnight were Hamas facilities in northern Gaza and a school in the city.
Palestinian President Mahmoud Abbas warned that the coming hours would be "dangerous and difficult" for the Palestinian people.
"I am afraid that what is to come is going to be dangerous because we can't bear another serious aggression and another occupation. Our people are living in a harsh way under the shelling and the air strike and the bombs but what is to come may be more difficult."
Egypt and other foreign mediators have been working to try to resolve the crisis, but Abbas said those efforts had yet to bear fruit.
"Regarding the soldier, we will surely reach an agreement. It is not a dead end. People want an acceptable solution and we are trying to find the solution."
Hamas has said earlier that the abducted Israeli soldier should not be freed without a prisoner swap, a demand which has been rejected by Israel.
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