In a briefing to the council, Tor Wennesland, the U.N. special coordinator for the Middle East peace process, said that humanitarian efforts to aid more than 2 million Gazans in dire need are “near the brink” of collapse, facing “nearly insurmountable challenges, amid displacement on an unimaginable scale.”

A vote on a final resolution, sponsored by the United Arab Emirates, is possible later Tuesday, according to U.N. officials. The goal, officials said, is obtaining U.S. agreement to vote yes, or at least for Washington to abstain to allow the measure to pass.

“We fully support addressing the humanitarian needs of the people of Gaza, as this resolution should set out to do,” State Department spokesman Matthew Miller said Tuesday. Negotiations “are very much ongoing. We are engaging constructively with our colleagues on the Security Council to resolve outstanding issues.”

The Biden administration has vetoed previous resolutions, arguing that a cease-fire ending Israel’s offensive in Gaza would effectively be a victory for Hamas, leaving its military capabilities in place and its top leaders alive. The United States has also objected to the lack of a specific condemnation of Hamas in earlier resolutions and the failure to include a declaration of Israel’s right to defend itself following the Oct. 7 attack that killed 1,200 people. The current version contains neither.

“It’s important for us that the rest of the world understand what’s at stake here. … What Hamas did on the 7th of October and how Israel has a right to defend itself against those threats,” White House National Security Council spokesman John Kirby told reporters Tuesday.

The draft “demands the immediate and unconditional release of all hostages” and access to address their medical needs. Although it directly criticizes neither Israel nor Hamas, referring to them only as “parties to the conflict,” the measure “firmly condemns all violations of international humanitarian law, including all indiscriminate attacks against civilians and civilian objects, all violence and hostilities against civilians, and all acts of terrorism.”

In recent visits to Israel by national security adviser Jake Sullivan and Defense Secretary Lloyd Austin, the Biden administration emphasized its continued support for the war’s aims. But it has also voiced increasing discomfort with Prime Minister Benjamin Netanyahu’s government as global condemnation builds over Washington’s refusal to call for an immediate humanitarian cease-fire.

The White House has pressured Israel to end what President Biden has called “indiscriminate” airstrikes and ground operations that have led to what Gazan health authorities have said are nearly 20,000 civilian deaths, and has asked for more “targeted” and “surgical” military operations against Hamas that avoid civilian casualties.

The three-page draft Security Council resolution calls for “urgent and extended humanitarian pauses and corridors throughout the Gaza Strip for a sufficient number of days to enable full, rapid, safe and unhindered humanitarian access” and to enable urgent rescue and recovery efforts.

It also demands the immediate and unconditional release of all hostages. An earlier, week-long pause in the fighting led to increased aid and the release of more than 100 Israeli and foreign hostages, leaving about 130 held by Hamas.

On Friday, Israel said it had recovered the bodies of three hostages in Gaza. On the same day, Israel Defense Force soldiers mistakenly shot and killed three additional hostages in the enclave.

The draft also establishes a monitoring mechanism, intended to speed up humanitarian aid deliveries, that turns over to the United Nations the current system of Israeli inspections of every truck entering Gaza. The U.N. mechanism was one of three options proposed to the council Monday by Secretary General António Guterres in a letter also seen by The Post. In addition to “a more robust United Nations presence on the ground,” Guterres alternatively suggested the establishment of “a civilian observer mission (deployed by the United Nations or a third party) … to monitor” aid shipments “with the consent or cooperation, as appropriate, of all relevant parties.” A third option was the deployment of unarmed U.N. military observers.

All of those proposals are likely to be strongly opposed by Israel, which does not currently hold a seat on the 15-member council.

The resolution “takes note” of Israel’s decision this week to open its Kerem Shalom crossing into Gaza to ease the current logjam through the Rafah crossing from Egypt — the only entry to the enclave that Israel does not control. But it also demands that all “parties … allow and facilitate the use of all land, sea and air routes to and throughout the entire Gaza Strip.”

Michael Birnbaum contributed to this report. This is a developing story.