Diplomats said Washington was concerned that the language wasn't airtight and therefore proposed the amendments.
Details of the final text were not disclosed in Washington or New York.
Negotiations on the draft have been going on in key capitals, with US Secretary of State Condoleezza Rice, French Foreign Minister Michel Barnier, and British Foreign Secretary Jack Straw trying to agree on wording that would allow the US to abstain rather than veto the resolution, the diplomats said.
A veto could be politically damaging because it would give the appearance that the US opposed the punishment of those responsible for atrocities in Darfur, the scene of perhaps the world's worst humanitarian crisis.
The widespread death and des-truction has been the result of a brutal counterinsurgency campaign led by government-supported Arab militias against black African rebels. The conflict began in February 2003, and the number of dead is now estimated at 180,000.
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