Introduced by Indonesia and Tunisia, the resolution risked not having nine out of 15 votes in its favor, the minimum required for adoption provided there is no veto by a permanent member, the diplomats told AFP.
Palestinian president Mahmud Abbas is set to take part Tuesday in a session on President Donald Trump's January 28 plan, which paves the way for Israeli annexation of much of the West Bank but also allows for a demilitarized Palestinian state.
The sudden Palestinian withdrawal of their request came after the United States -- which enjoys veto power as a permanent member -- proposed a series of amendments that could come for a vote at the session attended by Abbas.
In proposals seen by AFP, the United States would significantly alter the text to remove references to 1967 lines being the basis of peace.
It would also cut out a line stating that Jewish settlements built in the West Bank since 1967 are illegal, a position taken by virtually every country except the US and Israel.
The United States is also seeking to eliminate language that equated East Jerusalem with the occupied West Bank.
The Trump plan calls for recognition of the contested holy city as Israel's undivided capital, while establishing a Palestinian capital on its outskirts.
While recognizing that the Trump plan "departs from the internationally endorsed terms of reference and parameters," the US wants the resolution to state that the Security Council "welcomes discussion on this proposal to advance the cause of peace."
"Discussions are continuing on the text," a diplomat said on condition of anonymity.
Other diplomats cast doubt on whether a vote could take place at a later date, considering the wide divergences in positions.
Diplomats, however, said they had no reason to think Abbas' appearance would be scrapped.
No comments