A US official told the BBC that it had been considering an abstention, which would have allowed the motion to pass.
Israel then contacted Donald Trump's transition team to intervene, an Israeli official told Reuters.
Egypt's resolution called for Israel to stop building new settlements, which it said breached international law.
It was to have been voted on in the UN Security Council on Thursday, but Egypt withdrew it hours before the meeting was due to start.
The United States, which holds a veto at Security Council, has traditionally sheltered Israel from condemnatory resolutions by voting them down.
"Israelis deeply appreciate one of the great pillars of the US-Israel alliance: the willingness over many years of the United States to stand up in the UN and veto anti-Israel resolutions," said Israeli Prime Minister Benjamin Netanyahu earlier.
"I hope the US won't abandon this policy."
But there had been speculation that the Obama administration might change that strategy in the president's final month in office and allow Egypt's resolution condemning Israel to pass by abstaining from voting in the Security Council.
Earlier on Thursday, Mr Trump had urged the Security Council to defeat the resolution.
In a statement, the US president-elect said "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.
"This puts Israel in a very poor negotiating position and is extremely unfair to all Israelis."
After the postponement of the vote, an Israeli official told Reuters news agency that it had warned the Obama administration in advance that it would appeal to the president-elect if the US abstained, and confirmed that it had directly asked Mr Trump to intervene.
Egyptian President Abdel al-Sisi also spoke to Mr Trump by telephone. In a statement, Mr Sisi's office said the two leaders had agreed the new US administration should be given a chance to deal with the issue.
Mr Trump takes over as US president on 20 January.
However, four other members of the security council warned that if Egypt did not press ahead with its resolution, other member states would do so.
New Zealand, Venezuela, Malaysia, and Senegal said they reserved the right to move ahead with the vote.
None of the four are permanent members of the council, but are serving two-year terms.