The Gaza police operations room and a Palestinian health official say separate Israeli airstrikes hit the compound of Gaza City's main hospital and a nearby park, causing casualties.
The Israeli military had no immediate comment.
Camera crews were prevented from filming the area of impact at Shifa Hospital. Health official Ayman Sahabani says several people were wounded in the strikes.
Meanwhile, Secretary-General Ban Ki-moon is demanding an end to the violence in Gaza "in the name of humanity" and is accusing the leaders of Israel and Hamas of being irresponsible and "morally wrong" for letting their people get killed.
Ban urged Israeli Prime Minister Benjamin Netanyahu and Hamas leader Khaled Mashaal on Monday to demonstrate "political will" and "compassionate leadership" to end the suffering.
The U.N. chief reinforced the U.N. Security Council's call early Monday morning for "an immediate and unconditional humanitarian cease-fire."