The Palestine Liberation Organisation (PLO) has expressed readiness for a Gaza truce and Washington says Israel has sought help in calming a 22-day conflict that has killed nearly 1200 in the enclave.
But the Israeli government remained silent on the subject while continuing its bombardment on Tuesday, leaving scores more dead more than three weeks after launching a military offensive against rocket-firing militants.
US Secretary of State John Kerry said Israeli Prime Minister Benjamin Netanyahu had asked for fresh help from America in trying to broker a ceasefire.
"Last night we talked, and the prime minister talked to me about an idea and a possibility of a ceasefire. He raised it with me, as he has consistently," said Kerry.
The top US diplomat added that Netanyahu had said he "would embrace a ceasefire that permits Israel to protect itself against (Palestinian militants') tunnels and obviously not be disadvantaged for the great sacrifice they have made thus far".
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There was no Israeli government comment.
PLO secretary-general Yasser Abed Rabbo said after consultations with Hamas and Islamic Jihad, the two main militant groups in Gaza, that there was "willingness for a ceasefire and humanitarian truce for 24 hours".
A joint delegation headed by Palestinian President Mahmoud Abbas would travel to Cairo to take the next step.
"This is more proof that we have a unified Palestinian stand," Abed Rabbo said. "The delegation will head to Cairo under the PLO umbrella represented by President Mahmoud Abbas."
Hamas said so far it had not agreed to any new truce and was waiting for Israel to show its hand first.
"When we have an Israeli commitment ... on a humanitarian truce, we will look into it, but we will never declare a truce from our side while the occupation keeps killing our children," Hamas spokesman Sami Abu Zukhri said on Facebook.
Mohammed Deif, head of the movement's military wing, echoed his position.
"There is no ceasefire without the stop of the aggression and the end of the siege," he said in remarks aired on Hamas radio and television.
A series of ceasefires in recent days have failed to take hold, as both sides appeared more determined than ever to keep up the fighting.
The Israeli offensive, which began on July 8, has killed more than 1190 Palestinians, mostly civilians according to the United Nations, and injured over 7000.
Fifty-six lives have been lost on the Israeli side, all but three of them soldiers.
