The U.S. attempt to condemn Hamas and demand that the militant group stop firing rockets into Israel, using "airborne incendiary devices" and putting civilians at risk sparked a Palestinian-backed amendment sponsored by Bolivia.
A vote on whether to necessitate a two-thirds majority was to precede the vote on the actual resolution itself.
Prime Minister Benjamin Netanyahu's released a statement following the vote praising the countries that did vote to condemn Hamas despite the resolution's failure.
The two-thirds majority that prevented passage of the resolution was advanced by Kuwait on behalf of the Palestinian Authority, and approved by a 75-72 vote with 26 abstentions.
But before the vote on the USA draft resolution, Bolivian Ambassador Sasha Llorentty Soliz withdrew the amendment.
Danon said he has had discussions with some of the Arab ambassadors in the United Nations, and they are unhappy with the support Hamas is getting from Tehran, and the fact that the PA is cooperating with Iran, seen by some of these countries - such as Saudi Arabia - as their mortal enemy.
The Israeli diplomat also thanked his U.S. counterpart, Ambassador Nikki Haley, for her "close cooperation in fighting for the truth that led to the formation of an unprecedented coalition for Israel and against terrorism".
Saudi Arabia's UN Ambassador Abdallah Al-Mouallimi, reflecting the Arab view, said the USA resolution would "undermine the two-state solution which we aspire to".
Resolutions adopted by the General Assembly are non-binding, however, they carry political weight and are seen as a barometer of world opinion.
"The General Assembly has never said anything - not one thing - about Hamas, even when we all agree Hamas' behavior undermines any prospects for peace".
A number of States explained their reasons for voting against the resolution.
Palestinian President Mahmoud Abbas, whose Fatah party has been locked in a power struggle with Hamas, welcomed the resolution's defeat saying, "The Palestinian presidency will not allow for the condemnation of the national Palestinian struggle".
Before the final vote, Haley reminded the chamber that last Friday the General Assembly voted six times in one day to condemn Israel.
Both the United States and European Union have classified Hamas as a terrorist group. It also reaffirmed "unwavering support" for a two-state solution to the Israeli-Palestinian conflict - issues not included in the US draft.
The United States put forward the resolution as it prepares to unveil new peace proposals that the Palestinians have already rejected.
The vote was symbolically important because, from the time Haley arrived at the U.N.in January 2017, she has made a point of trying to turn the tide of what the Trump administration considers overwhelmingly anti-Israel resolutions and this vote illustrated what an uphill battle that turned out to be. And he said it would also turn attention away from Israel's occupation, settlement activities and "blockade" - whether in Gaza, the West Bank or east Jerusalem which the Palestinians want as their future capital.