The US, UN and Egypt are leading calls for a Gaza ceasefire, but there is no sign the violence is losing momentum.
In all, 81 Palestinians, about half of them civilians, had been killed by Monday morning (local time) and 720 had been wounded. Three Israeli civilians have died from Palestinian rocket fire and dozens have been wounded.
President Barack Obama said he was in touch with players across the region in hopes of halting the fighting. He warned of the risks of Israel expanding its five-day air assault into a ground war.
"We're going to have to see what kind of progress we can make in the next 24, 36, 48 hours," Obama said during a visit in Thailand.
UN chief Ban Ki-moon urged the two warring parties to achieve an immediate ceasefire. He said he was heading to the region to appeal personally for an end to the violence, but no date was given for his arrival.
Israeli TV stations said an Israeli envoy travelled to Cairo on Sunday and was returning to Israel with details of ceasefire proposals. Channel 2 TV, citing American diplomats, said Israeli Prime Minister Benjamin Netanyahu's personal envoy, Yitzhak Molcho, would visit Washington in the coming days.
Hamas officials said their supreme leader, Khaled Meshaal, held talks with Egyptian President Mohammed Morsi, and that Turkish Foreign Minister Ahmet Davutoglu was to visit Gaza on Tuesday.
Hamas is linking a truce deal to a complete lifting of the border blockade on Gaza imposed since Islamists seized the territory by force. Hamas also seeks Israeli guarantees to halt targeted killings of its leaders and military commanders. Israeli officials reject such demands.
They say they are not interested in a "time-out" and want firm guarantees that militant rocket fire into Israel will end.
On the ground, there were no signs of a letup in the fighting as Israel announced it was widening the offensive to target the military commanders of the ruling Hamas group.
The Israeli military carried out dozens of airstrikes throughout Sunday, and naval forces bombarded targets along Gaza's Mediterranean coast. Many of the attacks focused on homes where militant leaders or weapons were believed to be hidden.
Palestinian militants continued to barrage Israel with rockets, firing more than 100 on Sunday. Some 40 rockets were intercepted by Israel's US-financed "Iron Dome" rocket-defence system, including two that targeted Tel Aviv. At least 10 Israelis were wounded by shrapnel.
Israel's decision to step up its attacks in Gaza marked a new and risky phase of the operation, given the likelihood of civilian casualties in the densely populated territory of 1.6 million Palestinians. Israel started its offensive on Wednesday in what it said was an effort to end months of intensifying rocket fire from the Hamas-ruled Gaza Strip.