US Ambassador to the UN Susan Rice warned that Sudan's refusal to accept a map demarcating the border with South Sudan could lead to the resumption of “outright conflict”.
Ms Rice told reporters after a closed Security Council meeting that the United States is "deeply concerned" about the lack of urgency from both countries, but especially Sudan, in implementing an African Union roadmap aimed at averting a new war.
South Sudan won independence from Sudan last year as part of a 2005 peace treaty that ended decades of war between the mainly Muslim north and Christian and animist south that killed two million people.
The two countries drew close to all-out war earlier this year over the unresolved issues of oil revenues and their disputed border.
The Security Council endorsed the AU roadmap in May, with specific timelines. The council threatened to impose non-military sanctions if Sudan or South Sudan fail to implement its provisions.
Neither country met the original August 2 deadline, but the council extended it to September 22 after AU talks mediated by former South African president Thabo Mbeki resulted in an oil agreement in early August.
The row over the sharing of the two countries' once-unified oil industry prompted South Sudan to shut down its oil production in January after accusing Sudan of stealing its oil exports.
Ms Rice said it is disappointing that the Sudanese government insists it will not implement the provisional oil agreement until all outstanding issues have been resolved.
On the border issue, South Sudan has agreed to the AU map, but Ms Rice said the Sudanese government's continuing refusal to accept it is preventing the establishment of a demilitarised border zone between the two countries. She said it also "calls into question Khartoum's seriousness".