Egypt requested that the vote be postponed, one day after submitting the draft text to the council, a move that triggered immediate calls from Israeli Prime Minister Benjamin Netanyahu for a US veto to block the resolution.
A similar resolution was vetoed by the United States in 2011, and it remained unclear whether Washington would shift stance this time, possibly abstaining to allow the measure to pass, although without US support.
"I hope the US won't abandon this policy."
Israel launched a frantic lobbying effort to pressure Egypt to drop the bid and reached out to its supporters in the United States and at the Security Council for support.
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Israeli Ambassador Danny Danon said his government was deploying "diplomatic efforts on all fronts to ensure that this disgraceful resolution will not pass in the Security Council."
A UN diplomat, speaking on condition of anonymity, dubbed the Israeli lobbying a "diplomatic World War III" and a senior Security Council diplomat suggested that the motion could be buried indefinitely.
Trump, who campaigned on a promise to recognise Jerusalem as Israel's capital, bluntly said Washington should use its veto to block the resolution.
"The resolution being considered at the United Nations Security Council regarding Israel should be vetoed," he said in a statement.
"As the United States has long maintained, peace between the Israelis and the Palestinians will only come through direct negotiations between the parties, and not through the imposition of terms by the United Nations," he said.
"This puts Israel in a very poor negotiating position and is extremely unfair to all Israelis."
Trump has chosen as ambassador to Israel the hardliner David Friedman, who has said Washington will not pressure Israel to curtail settlement building in the occupied West Bank.
No new timeframe was announced for the vote, which had been scheduled for Thursday afternoon.
Arab ambassadors held an emergency meeting at the United Nations to press Egypt to move ahead with a vote but an Arab League committee decided after meeting in Cairo to continue talks on the fate of the motion.
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