The incursion late Friday triggered clashes with angry residents following a week of rising tensions.
Pro-Israel advocates hailed the decision, saying it confirmed the US recognised the whole of Jerusalem as part of Israel.
The United Nations and Egypt have not publicly detailed their proposals.
The General Assembly adopted a resolution with 120 votes in favour, eight against and 45 abstentions.
The protests tapered off around sunset when many demonstrators left border camps for the evening meal that breaks their fast during the Muslim holy month of Ramadan.
It was the third time President Mahmoud Abbas, 82, had been hospitalised in a week.
Netanyahu called for international condemnation of “anti-Semitism” by Abbas over remarks on Monday.
Tens of thousands of Palestinians began a six-week-long protest last Friday in tent encampments set up along the fenced border of the Israeli-blockaded Gaza Strip.
Citing security concerns, the Israeli military enforces a “no go” zone for Palestinians on land in Gaza adjacent to Israel’s border fence.
The Palestinian leader accused Ambassador David Friedman of defending Israeli settlers in the West Bank by saying that they were building on “their land”.
Kushner and Greenblatt are working on a new peace plan and met with the 15 Security Council ambassadors behind closed doors after the public meeting on Tuesday.
Palestinian officials have said they will not meet US Vice President Mike Pence when he visits Egypt, Jordan and Israel this month.
President Mahmoud Abbas thanked Donald Trump for hosting him at the meeting on the sidelines of the UN General Assembly gathering.
Trump praised Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas alike, saying both were ready for peace.
US President Donald Trump will meet Palestinian President Mahmoud Abbas in the West Bank town of Bethlehem on Tuesday.
The guidelines of the new government make no mention of a two-state solution to the Palestinian conflict.
A total of 135 countries recognise Palestine, including several east European nations.
The US has veto power as one of the council’s five permanent members & has pledged to block the move.
