A Security Council resolution requires a minimum of nine yes votes, with no vetoes by its permanent members, for passage.
About 120 Palestinians have been killed and hundreds wounded by Israeli forces along the fence that divides Israel from Gaza since the protests erupted at the end of March inside Gaza, an impoverished Mediterranean enclave where nearly two million Palestinians live.
A 21-year-old Palestinian health worker was killed on Friday, the Gaza Health Ministry said. No Israelis have been killed during the protests.
Israel has contended that its military is acting lawfully to stop the protesters from breaching the fence, and it has rejected accusations that soldiers have used deadly force needlessly. The Israelis have also accused Hamas and its militant affiliates in Gaza of using the protests as cover for sending attackers into Israel.
The United States has backed Israel completely on the Gaza issue.
The resolution by Kuwait, the only Arab member of the Security Council, called for the “consideration of measures to guarantee the safety and protection” of Palestinian civilians in Gaza and the Israeli-occupied West Bank, and for a halt to “the use of any excessive, disproportionate and indiscriminate force” by the Israeli military.
Ms. Haley, an outspoken supporter of Israel at the United Nations, called the draft a “grossly one-sided approach” that did not acknowledge any responsibility by Palestinian militants for the violence.
The diplomatic jousting after the votes at the Security Council meeting displayed the yawning divide and dual narratives of the Israeli and Palestinian sides.