More than 120 Palestinians have been killed by Israeli forces along the fence that divides Israel from Gaza since the protests erupted in March. The United States was the only country that voted against the text.
The resolution, introduced by Kuwait, was meant to respond to the escalation of violence in Gaza last month during protests at the border with Israel.
Israel's UN Ambassador, Danny Danon, condemned the Kuwaiti draft "as a hypocritical resolution that sought to condemn Israel while failing to even mention the terrorists of Hamas as the root cause of violence and unrest in our region".
The outcome deepened the deadlock at the top United Nations body over how to respond to the flareup of violence in Gaza that a United Nations envoy has warned is close to the brink of war.
The U.S. proposal, meanwhile, said nothing about Israeli force or protecting Palestinian civilians, while casting blame on Hamas for violence, endangering civilians, and deteriorating conditions in Gaza.
Hamas and other militants bombarded southern Israel with rockets and mortars Tuesday, and Israel responded by striking targets throughout Gaza.
United Nations envoy Nikki Haley said the US will veto an anti-Israel resolution over the ongoing Gaza tensions.
Since March 30, Israeli fire has killed more than 115 Palestinians, majority unarmed protesters, according to the Palestinian Health Ministry.
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The final version, however, urged UN Secretary-General Antonio Guterres to report within 30 days of its adoption on "ways and means for ensuring the safety, protection and well-being of the Palestinian civilian population".
It was the worst flareup since the 2014 war in Gaza.
The United States has backed Israel completely on the Gaza issue.
A draft resolution needs nine votes to be adopted by the 15-member council and no veto from the five permanent members - UK, China, France, Russia and the US.
During a second vote, the United States failed to win support for its own rival measure calling on Palestinian militants to halt their protests in Gaza and condemning Hamas.
The protests - dubbed "the Great Return March" - called for the right of return of refugees, and peaked on 14 May when the USA moved its embassy in Israel from Tel Aviv to the contested city of Jerusalem.
Najar, a 21-year-old volunteer medic, was shot as she ran toward the fortified border fence, east of the south Gaza city of Khan Younis, in a bid to reach a casualty, a witness said.
Shots were fired at an army vehicle and a Palestinian had crossed into Israel, planted a grenade and returned to Gaza, it said, stressing soldiers were acting "in accordance with the rules of engagement".