The UN chief and Washington's top diplomat are holding a flurry of meetings in Cairo to push for an end to two weeks of violence in Gaza that has killed 585 Palestinians.
As the conflict entered its third week, neither side showed any sign of willingness to pull back, with Israel pursuing a relentless campaign of shelling and air strikes, and militants hitting back with rocket fire and fierce attacks on troops operating on the ground.
Gaza medics say the Palestinian dead include many women and children, while on the Israeli side, 27 of the 29 victims were soldiers killed since a ground assault began late on July 17.
World powers have urged Hamas to accept an Egyptian-brokered ceasefire and stop raining rockets into Israel from the Gaza Strip, demands it has so far resisted.
Kerry opened talks with Egyptian Foreign Minister Sameh Shoukri and was later to meet the president, former military chief Abdel Fattah al-Sisi.
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The top US diplomat, who arrived late on Monday, held talks in Cairo on Monday with UN chief Ban Ki-moon, who has also come to the Egyptian capital to push for a truce.
Ban, who has demanded a complete halt to the bloodshed, was to hold separate talks with Sisi on Tuesday.
On Monday, Kerry demanded that Hamas agree to end the fighting to spare further bloodshed, in a call echoed by the Arab League.
"Only Hamas now needs to make the decision to spare innocent civilians from this violence," he said, pledging $US47 million ($A50.85 million) in humanitarian aid for the battered Gaza Strip.
Meanwhile, Hamas leader Khaled Meshaal and Palestinian president Mahmud Abbas held talks in Doha on Monday, pledging to work together for a ceasefire and to lift the blockade on Gaza.
Meanwhile, there was no halt to the bloodshed, with 25 people killed in fresh Israeli strikes on Tuesday, raising the death toll since Israel launched its operation on July 8 to 585, emergency services spokesman Ashraf al-Qudra said.
Another 3640 people have been wounded.
Israel has said Operation Protective Edge is to stamp out rocket fire from Gaza, and on July 17 it sent in ground troops to destroy cross-border tunnels used by Hamas militants to infiltrate southern Israel.
Since the offensive, more than 100,000 Gazans have fled their homes, seeking shelter in 69 schools run by the Palestinian refugee agency UNRWA.
Hamas's main condition for halting its fire is a lifting of Israel's eight-year blockade on the enclave, but it also wants "the release of those recently detained" in the West Bank, Ismail Haniya, the movement's top Gaza-based official, said late on Monday.
Cross-border rocket fire has continued despite the operation, with 116 rockets hitting Israel on Monday, one striking the greater Tel Aviv area, and another 17 shot down.
