The US has given up trying to win its soldiers immunity from prosecution at the new International Criminal Court.
The prisoner abuse scandal undermined support for the US
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.
The UK was one of the few countries that planned to back the US.
"The United States has decided not to proceed further with consideration and action on the draft at this time in order to avoid a prolonged and divisive debate," said the US deputy ambassador to the UN James
"We are dropping action on this
The US has previously threatened to veto UN peacekeeping operations if its demands for exemption from prosecution by the International Criminal Court (ICC) in The Hague were not met.
Mr Cunningham did not repeat the warning, but said the US would in future "need to take into account the risk of ICC review when determining contributions to UN authorised or established operations".
The US offered a compromise to the Security Council on Tuesday, asking it to renew the existing immunity for just one more year.
But it was not enough to gain the necessary support of nine out of the 15 council members.
Earlier this month Mr Annan said if the exemption - which expires on 30 June - were extended, it would discredit the UN's claim to represent the rule of law.
"For the past two years, I have spoken quite strongly against the exemption and I think it would be unfortunate for one to press for such an exemption, given the prisoner abuse in Iraq," he said.
"Blanket exemption is wrong. It is of dubious judicial value and I don't think it should be encouraged by the council."
It is unlikely that American troops would end up at the ICC when the exemption runs out next week, our correspondent says.
Ninety-four countries, including Iraq, have not signed up so it would not apply to US troops on their territory.
Washington also has bilateral agreements with 89 others to protect US troops from prosecution.
Our correspondent says the countries signed up to the ICC point out that the court is only meant to be a measure of last resort, to be used if US courts failed to take action themselves.