Israeli aircraft and tanks have hit more than 70 targets in the Gaza strip, including five mosques, a football stadium and the home of the late leader of Hamas' military wing, according to Palestinian police.
At least seven Palestinians were reported killed in the new round of air strikes early on Tuesday, bringing the death toll of Israel's two-week assault on the Gaza Strip to more than 580.
Police spokesperson Ayman Batniji said tank shells damaged several houses along the eastern border of the territory and that at least 19 fishing boats were destroyed by navy shells fired from the Mediterranean.
Al Jazeera's Stefanie Dekker, reporting from Gaza City, said artillery shelling continued on Tuesday morning, especially near the eastern border areas.
"Israeli tanks are stationed about 700 to 800 metres away from the borders and are expected to continue to come closer," she said.
The intense Israeli bombardment came as UN chief Ban Ki-moon and US Secretary of State John Kerry met in Cairo to launch the highest-level push yet to end the two weeks of violence.
The death toll in Israel’s 14-day offensive climbed to more than 583 Palestinians, including dozens of women and children. More than 3,600 others have been injured.
The Israeli military on Tuesday said two soldiers were killed the day before by rockets fired from Gaza, bringing the Israeli toll to 27 troops and two civilians in the bloodiest Gaza conflict since 2009.
Kerry said he was hoping to get international support in Washington's push for a ceasefire, while acknowledging that the differences between Israel and Hamas run deep and must be addressed in any long-term solution.
"We will work to see if there is some way to not only arrive at a ceasefire of some kind but to get to a discussion about the underlying issues," Kerry said at the start of the meeting with the UN chief.
Kerry pledged $47 million in humanitarian aid to Gaza.
Washington reiterated that Israel had the right to defend itself against a barrage of more than 1,500 rockets launched by Hamas, while voicing concern about civilian casualties.
US President Obama said Israel's military assault of Gaza had already done "significant damage" to Hamas' network of tunnels, safe havens and other infrastructure as he talked of the need for a ceasefire.
"We have serious concerns about the rising number of Palestinian civilian deaths and the loss of Israeli lives," Obama said in Washington.
UN chief Ban, meanwhile, appealed for the violence to "stop now" as it emerged that most of the dead were civilians.
Kerry, Ban, and Arab League chief Nabil al-Arabi in Cairo urged Hamas to accept an Egyptian-proposed ceasefire.
Conditions for ceasefire
Hamas insisted on a lifting of Israel's siege of Gaza and the release of prisoners in order to agree to any truce accord.
"The conditions for a ceasefire are... a full lifting of the blockade and then the release of those recently detained in the West Bank," its leader in Gaza, Ismail Haniya, said on television.
"We cannot go backwards, to a slow death," he said, referring to the Israeli blockade in force since 2006.
Khaled Meshaal, the leader of Hamas' political bureau, held talks with Palestinian President Mahmoud Abbas in Doha, the Qatari capital, on Monday. The two pledged to work together for a ceasefire and to lift the blockade on Gaza.
Monday's attacks across Gaza killed at least 103 people. In the costliest single Israeli bombardment, an air strike hit a residential tower block in central Gaza City, killing 11 people, including five children.
It came after Israeli tank shells struck a hospital in Deir al-Balah, killing at least five people, including doctors and two patients who died in their hospital beds, officials said, indicating that at least 70 people were wounded.
Rights group Amnesty International said that the shelling of the hospital as well as the "continuing bombardment of civilian homes" in Gaza "add to the list of possible war crimes that demand an urgent independent international investigation."
Since the Israeli operation began on July 8, huge numbers of Palestinians have fled their homes, with the UN saying more than 100,000 people have sought shelter in 69 schools run by its Palestinian refugee agency, UNRWA.