The Council, which late Tuesday authorised sanctions against Sudan, was considering a French resolution that would bring the war crimes before the ICC, which is not recognized and opposed by the United States.
But Washington said it wanted to propose some changes and France agreed, putting off any vote.
"We are in a situation where there are still ongoing discussions between council members," US envoy Stuart Holliday told reporters. A senior US official in Washington said a vote could come Thursday.
The United States could veto a resolution, a move that carries political risk after the United States pushed to bring the Darfur atrocities to worldwide attention and called it "genocide".
Deputy State Department spokesman Adam Ereli said talks were continuing in an effort to "produce something that everybody could support."
"We are working with our other partners in the Security Council to fashion a resolution that we can support that meets both our goal of accountability and is consistent with our policy on the ICC," he said.
The United States opposes the The Hague-based ICC, fearing it could become a prime target as it carries out many peacekeeping operations, but has got little support for its counter-proposal for an ad-hoc court in Tanzania.
"My understanding is that we're all pitching in there to try and make sure this resolution, when it's put to a vote, actually passes," said Britain's UN ambassador, Emyr Jones Parry.
"The British position is very clear. We want that referral to the ICC," he said.
The 15-member council voted unanimously last week to approve a 10,000-strong peace force for southern Sudan to monitor the January accord that ended the country's 21-year north-south civil war.
But there are sharp disagreements on how to handle Sudan's western region of Darfur, where a new report on Wednesday said an estimated 300,000 people have died from a separate conflict between rebels and government-backed militias.
The council voted 12-0 to slap new sanctions on Sudan but the United States could not get unanimous support as Algeria, China and Russia abstained.
The resolution allows for the seizure of assets and a travel ban against individuals who commit atrocities, impede the peace process in Darfur or "constitute a threat to stability" in the region.
Violators will be identified by a new committee that will include all 15 Security Council members.
The resolution also extended an existing arms embargo in Darfur to the Sudanese government and specifically prohibited Khartoum from offensive military flights into the region.
In Khartoum, the Sudanese foreign ministry blasted the measure as "unbalanced and inappropriate," saying it ignored government efforts to stop the violence.
Violence in Darfur exploded when rebels in the western Sudanese region rose up against the government in February 2003.
The government put down the rebellion with the help of proxy militias known as Janjaweed, which have been accused of widespread murder, rape and pillaging.
Richard Dicker, who heads the international justice division of Human Rights Watch, said talks with Sudanese government leaders had shown that Khartoum takes the threat of ICC prosecution "very seriously."
The proposed resolution "sends a real clear message -- that they are sensitive to in Khartoum -- that those most responsible will be held to account," Dicker said. "And that's the message this council needs to send."