France and Britain are reportedly working, with US backing, on draft resolutions intend to be submitted to the UN Security Council for a binding vote aimed at ending the fighting in the South.
The US has veto power at the United Nations Security Council and any resolution would need its active or tacit support.
Jordan, separately from the European states, has attempted to pass a resolution on the Gaza conflict since July, with little success.
The UN Security Council on Wednesday expressed "grave concern" at the resumption of hostilities in Gaza between Israel and Palestinians and called upon the parties to resume negotiations to urgently reach a "sustainable and lasting ceasefire."
The 15-member Security Council also "called upon the parties to prevent the situation from escalating and to reach an immediate humanitarian cease-fire," said British UN Ambassador Mark Lyall Grant, president of the council for August.