Algeria put forward an initial draft resolution more than two weeks ago. But US Ambassador to the UN Linda Thomas-Greenfield quickly said the text could jeopardize "sensitive negotiations."
The UN Security Council had been due to vote on a brief draft resolution on Friday morning, but it was delayed at the request of the United Arab Emirates.
The US said it supported the resolution but did not vote for it because the text failed to condemn Hamas.
The newly appointed ambassador to Israel has drawn praise from both right and left. But his record in the Obama administration should raise concerns.
Both countries submitted resolutions to the UNSC on the Gaza war and the October 7 Hamas assault on Israel.
It was not immediately clear if or when the United States planned to put the draft resolution to a vote.
The two proposals were put forward after the UNSC on Friday held its second closed-door consultation this week on the Gaza violence.
The PA envoy Riyad Mansour wrote to British Ambassador Barbara Woodward asking for a Security Council meeting and demanding action to “hold Israel accountable for its crimes” in Jenin and elsewhere.
The presidency of the security council is a rotating one-month position for the 15 members of the council; of which 10 are non-permanent members.
Abbas also equated statements by Israeli officials with those of the infamous Nazi propagandist Joseph Goebbels.