GAZA CITY, Gaza Strip (AP) -- A high-level attempt by the U.N. chief and the U.S. secretary of state to end deadly Israel-Hamas fighting was off to a rough start Monday: Gaza's Hamas rulers signaled they won't agree to an unconditional cease-fire, Israel's prime minister said he'll do whatever is necessary to keep Israelis safe from Hamas attacks and the overall Palestinian death toll surpassed 560.
Across Gaza, Israeli fighter planes hit homes and a high-rise tower, burying families in the rubble. The strike on the Gaza City tower brought down most of the building, killing 11 people -- including six members of the same family -- and wounding 40, said Palestinian health official Ashraf al-Kidra.
Israeli tanks, meanwhile, shelled a hospital in central Gaza, killing four people and wounding dozens as the daily death toll surpassed 100 for a second day. Israel said the shelling targeted rockets hidden near the compound, and accused militants of using civilians as shields.
At least 565 Palestinians have been killed and more than 3,600 wounded in the past two weeks, al-Kidra said.
On the Israeli side, seven more soldiers were killed in clashes with Gaza fighters Monday, bringing the military death toll to 25 -- more than twice as many as in Israel's last Gaza ground war in 2009.
Two civilians have also died in Palestinian rocket attacks on Israeli cities and scores of soldiers have been injured.
The mounting bloodshed brought U.N. Secretary-General Ban Ki-moon and U.S. Secretary of State John Kerry to Cairo on Monday, for a new cease-fire push. However, the gaps remain wide and no credible mediator has emerged.
Egypt, Israel and the U.S. back an unconditional cease-fire, to be followed by talks on a possible new border arrangement for Gaza. Israel and Egypt have severely restricted movement in and out of Gaza since Hamas seized the territory in 2007.
Hamas, with some support from Qatar and Turkey, wants guarantees on lifting the blockade before halting fire. The Islamic militant group has no faith in mediation by Egypt's rulers, who deposed a Hamas-friendly government in Cairo a year ago and tightened restrictions on Gaza -- to the point of driving Hamas into its worst financial crisis since its founding in 1987.
The top Hamas leader in Gaza, Ismail Haniyeh, said Monday that Gaza's 1.7 million people share Hamas' goal of forcing Israel and Egypt to lift the blockade.
"We cannot go back, we cannot go back to the silent death" of the blockade, he said. "Gaza has decided to end the blockade by its blood and by its courage."
After a meeting with Egyptian Foreign Minister Sameh Shukri, Ban said that "violence must stop by all sides," and that they must enter negotiations, seemingly siding with Cairo's approach.
However, Ban also said: "We can't claim victory simply by returning matters to where they stood before they led to terrible bloodshed."
The border blockade has set Gaza back years, wiping out tens of thousands of jobs through bans on most exports and on imports of vital construction materials Israel says could be diverted by Hamas for military use.
Israel allows many consumer goods into Gaza, but experts say Gaza's economy cannot recover without a resumption of exports.
The Rafah passenger crossing with Egypt is Gaza's only gate to the world, but Egypt has tightened restrictions over the past year, allowing only medical patients, Muslim pilgrims and Gazans with foreign passports to travel.
On Monday, President Barack Obama reaffirmed his belief that Israel has the right to defend itself against rockets being launched by Hamas into Israel. Yet, he contended that Israel's military action in Gaza had already done "significant damage" to the Hamas terrorist infrastructure and said he doesn't want to see more civilians getting killed.
As Obama spoke, Kerry flew to Cairo to join diplomatic efforts to resume a truce that last had been agreed to in November 2012.
Kerry headed almost immediately into a meeting with Ban, where he announced the U.S. will send $47 million in humanitarian aid for tens of thousands of Palestinians who have fled their homes in Gaza to escape the violence. Kerry's top aides warned, however, that achieving an immediate and lasting cease-fire would be difficult and he hoped to make any progress over the next several days to secure even a temporary pause in the bloodshed.
It's not clear exactly what Israel and Hamas would each demand in return for agreeing to a truce now, but senior State Department officials said the issue of opening border crossings -- potentially into Israel and Egypt -- was under discussion.