US House of Representatives speaker Paul Ryan and Republican Senator John McCain have slammed the Obama administration's decision to abstain in the UN Security Council vote.
In a statement, Ryan said the decision was "absolutely shameful" and a "blow to peace".
Meanwhile McCain said the move "has made us complicit in this outrageous attack."
Israeli Energy Minister Yuval Steinitz has said the US has abandoned Israel by abstaining in a UN Security Council vote demanding an end to Israeli settlements.
He told Channel Two News: "This is not a resolution against settlements, it is an anti-Israel resolution, against the Jewish people and the state of the Jews. The United States tonight has simply abandoned its only friend in the Middle East."
The US Ambassador to the UN has said Israel's continued settlement building "seriously undermines Israel's security".
Washington allowed the UN Security Council to adopt a resolution by abstaining from the vote.
Samantha Power told the council after the vote: "The United States has been sending a message that the settlements must stop privately and publicly for nearly five decades.
"One cannot simultaneously champion expanding Israeli settlements and champion a viable two state solution that would end the conflict. One had to make a choice between settlements and separation."
The UN Security Council has passed a resolution demanding Israel stop building settlements on occupied Palestinian territory.
The resolution was put forward at the 15-member council by New Zealand, Malaysia, Venezuela and Senegal.
Egypt withdrew from voting on Thursday after coming under pressure from Israel.
The US abstained after Donald Trump called on the country to veto the measure.
The motion was adopted with 14 votes in favour to a round of applause.
Donald Trump will nominate bankruptcy attorney David Friedman as the US ambassador to Israel, the President-elect's team said in a statement.
"(Friedman) has been a long-time friend and trusted adviser to me. His strong relationships in Israel will form the foundation of his diplomatic mission and be a tremendous asset to our country as we strengthen the ties with our allies and strive for peace in the Middle East," Trump said in the statement.
Friedman said he would work tirelessly to "strengthen the unbreakable bond between our two countries and advance the cause of peace within the region, and look forward to doing this from the U.S. embassy in Israel’s eternal capital, Jerusalem."
The US embassy has for decades been located in Tel Aviv.
Trump had pledged during the presidential campaign to move it to Jerusalem, a move almost certain to provoke objections from Muslims around the world.
The United States and other powers do not regard Jerusalem as Israel's capital and do not recognise Israel's annexation of Arab East Jerusalem following its capture in the 1967 Middle East war.
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Israeli Prime Minister Benjamin Netanyahu believes he and newly elected US President Donald Trump can work together to bring relations between the two countries to "new heights".
In a statement congratulating the Republican candidate, Netanyahu said: "President-elect Trump is a true friend of the State of Israel, and I look forward to working with him to advance security, stability and peace in our region.
"I am confident that President-elect Trump and I will continue to strengthen the unique alliance between our two countries and bring it to ever greater heights," said the right-wing leader, who has had a rocky relationship with outgoing Democratic President Barack Obama.