US President Joe Biden and administration officials have encouraged Prime Minister Benjamin Netanyahu and other top Israeli officials to wind down the bombardment of Gaza.
It comes as the Israeli and Palestinian death tolls mounted and pressure grew on Mr Biden to move more forcefully to stop the fighting.
Top administration officials underlined to the Israelis time is not on their side in terms of international objections to nine days of Israeli airstrikes and Hamas rockets, and that it is in their interest to wind down the operations soon.
This was according to an official, who was not authorised to comment publicly on the private talks and spoke on condition of anonymity.
The account shows Biden administration officials going further privately in messaging to Mr Netanyahu than they have previously revealed.
A White House readout of a call to Mr Netanyahu on Monday said Mr Biden had expressed support for a cease-fire, but said nothing about the US urging Israel to bring fighting to a close.
The fighting has killed at least 213 Palestinians and 12 people in Israel, and tested both Mr Biden’s reluctance to publicly criticise Israel and his administration’s determination not to bog down its foreign policy focus in Middle East hot spots.
The Palestinian ambassador to the United Nations on Tuesday challenged the Biden administration to show any results from what it is calling its quiet diplomacy to stop the new Israeli-Hamas battles.
Ambassador Riyad Mansour pointed to the US repeatedly blocking a UN Security Council action on the conflict, and he urged the Biden administration to do more.
He said: “If the Biden administration can exert all of their pressure to bring an end to the aggression against our people, nobody is going to stand in their way.”
France, in consultation with Egypt and Jordan, on Tuesday was preparing a UN Security Council resolution calling for a cease-fire, Zhang Jun, China’s UN ambassador, and other diplomats told reporters.
The move to put the UN’s most powerful body behind a demand for Israel and Hamas to stop hostilities came after the US repeatedly blocked what would have been a unanimous Security Council statement expressing concern about the fighting.
The White House has so far resisted the calls for ramping up public pressure on Mr Netanyahu.
It has made the calculation that Israelis will not respond to international resolutions or public demands by the US and that its greatest leverage is behind-the-scenes pressure, according to the person familiar with the administration’s discussions.
The person said that the Israelis have signalled that it is possible their military campaign could end in a matter of days.