The deaths in Khan Younis, Beit Hanoun and Beit Lahiya raised the Palestinian toll to 539 killed, including nearly 100 children and many other civilians, since the offensive was launched on July 8, Gaza health officials said.
Israel’s death toll also rose to 29, with two soldiers killed in the past day of fighting, the Israeli military said. The total includes two civilian killed by rocket fire.
Violence also spread to the occupied West Bank, where medics said soldiers shot and killed a Palestinian man while dispersing protesters throwing stones at a military jeep.
Israel said a Palestinian shot at a car and seriously wounded an Israeli in the Nablus area on Tuesday.
Kerry arrived in Cairo on Monday and, during talks with United Nations Secretary-General Ban Ki-moon, said the United States would provide $47 million in humanitarian aid for Gaza.
Washington is “deeply concerned about the consequences of Israel’s appropriate and legitimate effort to defend itself,” Kerry said. “No country can stand by when rockets are attacking it.”
“But always, in any kind of conflict, there is a concern about civilians – about children, women, communities that are caught in it,” Kerry said.
A senior State Department official said on Kerry’s flight to Cairo that Washington’s goal was to “achieve a cessation of hostilities as soon as possible,” but that the process would be difficult with the sides far apart on terms for a truce.
Kerry plans to stay in Cairo until Wednesday morning and has no currently scheduled end to his regional trip, which may include talks with officials from Qatar, a Gulf state which has relatively close ties to the Islamist Palestinian group Hamas and hosts its leader, Khaled Meshaal.
Israel Radio said Islamic Jihad militants in Gaza said the sides may agree to a five-hour humanitarian truce on Tuesday to allow civilians to stock up on vital supplies.
Ban was scheduled to fly to Israel on Tuesday for talks with Prime Minister Benjamin Netanyahu and also to meet Palestinian officials in the West Bank.
Egypt presented a ceasefire plan last week. Israel accepted, but Hamas rejected it, saying the group had not been consulted.
An Israeli official in Washington, who declined to be named, said he wanted Kerry to get Egypt to apply pressure on Hamas.