US Ambassador John Danforth, however, said after a closed-door council meeting on Thursday he expected the draft to be adopted perhaps next week with some revisions.
China threatened to use its veto power against the resolution if changes were not made in the text, objecting mainly to the specific sanctions threats.
"The draft as it stands right now will not be acceptable," Chinese Ambassador Wang Guangya said.
A minimum of nine votes and no veto is needed for adoption in the 15-member council.
The resolution, which calls for an expanded African force, threatens punitive measures "in the petroleum sector" as well as against individual Sudanese officials if violence continues in Darfur, or Khartoum does not cooperate with the monitors.
African Union role
Though objecting to oil sanctions, the council members backed a large African Union force in the western region.
"I am very encouraged by the meeting," Danforth said. "The importance of getting an outside presence into Darfur to monitor the situation is something that is impossible to overstate".
Nigerian President Olusegun Obasanjo, who has been conducting peace talks on Sudan for the African Union, has said the 53-nation alliance would "enhance and augment" its monitoring mission in Darfur.
Sudan earlier rejected the US declaration.
"This is just another sort of pressure brought against the government of Sudan by the United States and Western governments, the kind of general political pressure that shows the US is not a friend of Sudan," said Ahmad Hasan al-Zubair, Sudan's finance minister.
"We will prove that it is true that the conflict in Sudan is an internal tribal problem and it will be for the national government to solve this problem," he said on leaving an African Union summit in Burkina Faso on Thursday.
However, a spokesman for the rebel Sudan Liberation Movement (SLM), Abd Al-Hafiz Mustafa Musa, hailed the US move as "a welcome development".
Pakistani Ambassador Munir Akram and Algerian Ambassador Abd Allah Baali said they strongly opposed the resolution, including the sanctions threat as well as a provision calling for UN Secretary-General Kofi Annan to set up an inquiry that would determine if genocide had taken place.
Russia and Angola also raised concerns, diplomats said.
France also questioned the need for sanctions threats at this time. A European Union fact-finding mission early this year concluded that while there was widespread violence in Darfur, it did not amount to genocide.
The 1948 UN Convention on the Prevention and Punishment of Genocide defines genocide as an intentional act to destroy, in whole or in part, a national, ethnical, racial or religious group.