The US has given up trying to win its soldiers immunity from prosecution at the new International Criminal Court.
United Nations Secretary General Kofi Annan had warned the Security Council not to renew the measure, partly because of the prisoner abuse scandal.
Washington withdrew its resolution after it became clear it would not get the required support.
For the last two years it had secured special status for US troops, arguing they could face malicious prosecutions.
The BBC's Susannah Price at the United Nations says the latest move is a major climb-down for the Americans, who rarely face such united opposition on the Council.
Good news for the rule of law and good news for cutting back impunity. Impunity is central to the practice of torture, whether it's an outgoing dictatorship 'decreeing itself amnesty, the White House decreeing itself above the law, or any government decreeing that despite the Torture Convention's ban on exceptional circumstances there are exceptional circumstances.
Australia has signed an Article 98 impunity accord which exempts US forces from the ICC's jurisdiction. We should abrogate that accord, especially as it grants legal protections to US troops which are not available to ADF troops.