At least 120 Palestinians have been killed and more than 3,800 wounded by Israeli fire in protests along the border.
The U.N. General Assembly approved a Palestinian-backed resolution Wednesday blaming Israel for violence in Gaza and deploring its "excessive use of force", after narrowly rejecting a US demand to add a condemnation of attacks on Israel by Gaza's Hamas rulers.
The US failed to win enough votes in its proposal to amendment a resolution, which would condemn Hamas for inciting violence.
Arab and Islamic nations then made a decision to seek a vote on virtually the identical resolution at Wednesday's emergency meeting of the General Assembly, where there are no vetoes.
On 1 June, the United States vetoed a Kuwait-drafted UN Security Council resolution that condemned Israel's use of force against Palestinian civilians, criticising it as a "grossly one-sided" view that failed to blame Hamas for the recent violence.
"We had more countries on the right side than the wrong side", Haley said in a statement. It also seeks recommendations to protect Palestinian civilians.
When the voting tally on the original resolution produced the more familiar United Nations split of 120 in favor, 8 against, and 45 abstentions, there was relieved applause from the Palestinian delegation. "It blames everything on Israel", Haley said.
"We need protection of our civilian population", Palestinian UN envoy Riyad Mansour told the General Assembly before the vote, adding that the resolution was "intended to contribute to a de-escalation of the volatile situation".
The permanent observer of the Palestinian mission to the United Nations, ambassador Riyad Mansour said that the USA amendment was offered in "bad faith" and said that the "illegal, belligerent, military occupation is the primary source and root cause of the recurrent and emergent crises we face".
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The resolution adopted Wednesday 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". "Is that a crime to ask for?".
The resolution's text deplores "any excessive use of force" by Israeli forces, particularly in Gaza, and demands that Israel "refrain from such actions".
The almost identical resolution proposed by Kuwait was vetoed by the USA in the Security Council on Tuesday.
Unlike the Security Council, resolutions adopted by the assembly are non-binding and there is no veto.
Israel's U.N. Ambassador Danny Danon said they "welcome the American amendment condemning the terrorists of Hamas".
"We can not remain silent in the face of the most violent crimes and human rights violations being systematically perpetrated against our people", Mansour said.
Voting with the United States and Israel were Australia, the Marshall Islands, Micronesia, Nauru, Solomon Islands and Togo. Last month the Palestinians urged the International Criminal Court in The Hague to launch an investigation into Israeli policies and actions in the West Bank, east Jerusalem and Gaza Strip, accusing Israel of systemic crimes.
The amendment offered by USA envoy Nikki Haley sought to condemn Hamas, which runs the elected government in Gaza, for firing rockets at Israel.