The overall Palestinian death toll passed 560 as high-level attempts to end Israel-Hamas fighting hit serious problems.
As the United Nations and US secretary of state John Kerry stepped up diplomatic efforts, Gaza's Hamas rulers signalled they will not agree to an unconditional ceasefire.
And Israel's prime minister Benjamin Netanyahu said he will do whatever is necessary to keep Israelis safe from Hamas attacks.
Across Gaza, Israeli fighter planes hit homes and a tower block, burying families in the rubble.
The strike on the Gaza City tower block 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, Mr al-Kidra said.
On the Israeli side, seven more soldiers were killed in clashes with Gaza fighters yesterday, 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 UN Secretary-General Ban Ki-moon and Mr Kerry to Cairo, for a new ceasefire push. However, the gaps remain wide and no credible mediator has emerged.
Egypt, Israel and the US back an unconditional ceasefire, 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 senior Hamas leader in Gaza, Ismail Haniyeh, said that Gaza's 1.7 million people share Hamas' goal of forcing Israel and Egypt to lift the blockade.
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.
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.
US President Barack Obama reaffirmed his belief that Israel has the right to defend itself against rockets being launched by Hamas into Israel.
But he contended that Israel's military action in Gaza had already done "significant damage" to the Hamas terrorist infrastructure and said he does not want to see more civilians getting killed.
As he spoke, Mr Kerry flew to Cairo to join diplomatic efforts to resume a truce that last had been agreed to in November 2012.
Mr Kerry's top aides warned, however, that achieving an immediate and lasting ceasefire would be difficult.
Mr Kerry is expected to meet senior Egyptian officials, including President Abdel Fattah al-Sisi and Arab League President Nabil Elaraby over the next few days.
But there were no immediate plans for face-to-face meetings with officials from Qatar, Turkey, Israel and the West Bank, and the State Department aides said it remained uncertain what could be accomplished in the talks.
Mr Netanyahu told Sky News Arabia that the goal of Israel's strikes on Gaza is "to restore quiet and security for the people of Israel for a significant period of time".
He added: "We'll take whatever action is necessary to achieve that goal."
Israel has said it is trying to minimise civilian deaths and has accused Hamas of using civilians as human shields.
However, Israeli strikes on homes have driven up casualties.
About half of the dead were killed in their homes, according to the Al Mezan Centre for Human Rights, a Palestinian human rights group.
Various Palestinian rights groups estimated that at least 425 homes across Gaza were attacked by the military since July 8.
Among the dead in the strike on the Gaza City tower block was Zakariya Abu Dagha, a leader of the Democratic Front for the Liberation of Palestine, one of several small PLO factions.
The Israeli military reported heavy fighting with Hamas in Gaza yesterday.
Three soldiers were killed in those clashes, while a female suicide bomber was shot before she could detonate her explosive belt among soldiers, the military said.
Another four Israeli soldiers were killed in a firefight when Hamas militants sneaked into Israel through a tunnel from Gaza.
The militants popped out of the ground close to an Israeli community near the border with Gaza before they were spotted by the military, the army said. Israeli media said 10 Hamas fighters were killed.
Since Israel's ground operation in Gaza began last week, Israeli soldiers have uncovered 45 shafts leading into about 16 underground tunnels, some as deep as 90 feet, the military said.
Israel says the tunnels, some starting from homes and mosques, are a strategic threat because they reach inside Israel and demolishing them is a high priority
Gaza militants have fired more than 2,000 rockets at Israel in the past two weeks, including 130 yesterday, the army said.