The Palestinians and its supporters are asking an emergency meeting of the UN General Assembly on Wednesday to adopt a resolution deploring Israel's "excessive use of force", particularly in Gaza.
The US is demanding changes, saying Israel is unfairly singled out in the draft, which also calls on UN officials to come up with recommendations for protecting Palestinian civilians.
Arab nations decided to go to the 193-member assembly, where there are no vetoes, after the US vetoed almost the same resolution in the Security Council on June 1. US Ambassador Nikki Haley called that Kuwait-sponsored resolution "grossly one-sided" for criticising the use of force by Israel, while not mentioning the Islamic militant group Hamas, which rules Gaza.
Ms Haley sent a letter to all UN member states on Tuesday calling the proposed General Assembly resolution "fundamentally imbalanced" for "ignoring basic truths about the situation in Gaza" and not mentioning Hamas.
She proposed an amendment condemning Hamas for firing rockets into Israel and inciting violence along the Gaza-Israel border fence, "thereby putting civilians at risk". The proposal also would condemn the diversion of resources in Gaza to building tunnels to infiltrate Israel and equipment to fire rockets and express "grave concern" at the destruction of the Kerem Shalom crossing point to Israel "by actors in Gaza".
Ms Haley said the amendment "is not controversial" and simply condemns "behaviour we should all recognise as harmful to the Palestinian people".
The letter said the amendment would be voted on before the resolution.
Palestinian Ambassador Riyad Mansour said on Tuesday night that he is lobbying 191 member states – all but the US and Israel – and expects to win.
While Security Council resolutions are legally binding, General Assembly resolutions are not, although they do reflect international opinion.
The Palestinians sought a Security Council resolution after Israel's military killed civilians during mass protests in Gaza aimed at the border blockade imposed by Israel and Egypt in 2007, after Hamas overran the territory.
Since the near-weekly protests began on March 30, more than 120 Palestinians have been killed and more than 3,800 wounded by Israeli army fire. The overwhelming majority of the dead and wounded have been unarmed, according to Gaza health officials. Israel says Hamas has used the protests as cover for attacks on the border fence.
The marchers have also pressed demands for a "right of return" for descendants of Palestinian refugees to ancestral homes in what is now Israel. More than 700,000 Palestinians were expelled or fled in the 1948 war over Israel's creation. Two thirds of Gaza's two million residents are descendants of refugees.
The draft General Assembly resolution demands that Israeli forces stop "any excessive, disproportionate and indiscriminate force". It calls for "immediate steps towards ending the closure and the restrictions imposed by Israel on movement and access into and out of the Gaza Strip".
It also "deplores the firing of rockets from the Gaza Strip against Israeli civilian areas", but doesn't say who is doing the firing.
The draft asks UN Secretary-General Antonio Guterres to make proposals within 60 days "on ways and means for ensuring the safety, protection and well-being of the Palestinian civilian population under Israeli occupation", including "recommendations regarding an international protection mechanism".
Standing with a half dozen Arab and Islamic supporters on Friday, the Palestinian ambassador said Mr Guterres "should utilise all the tools available to him in the [UN] Secretariat and on the ground, and with all of the collective mind of all of us who are ready and willing to help in any possible way".