A senior US senator has said Sudan's government has assured him it will hold a referendum on independence for the south and is committed to the outcome.
John Kerry added that Sudan - which is under US sanctions - could benefit in important ways if it kept that promise.
The chairman of the Senate foreign relations committee was speaking after a three-day visit to the country.
Earlier, Sudan's president said the referendum should lead to further negotiations between north and south.
"It is without doubt a crucial event that is mixed with anxiety due to its importance and historical significance," Omar al-Bashir said.
"No matter what the outcome of the referendum will be, it will result in a new situation that will require consultations and negotiations with the peace partner."
The vote - due on 9 January - is the result of the 2005 Comprehensive Peace Agreement (CPA), which ended the 21-year civil war between north and south, which left an estimated 2 million people dead.
The BBC's James Copnall in Khartoum says Sudan has been subject to US sanctions since 1997, and the economic impact on the country is of great concern to President Bashir and his ruling National Congress Party.
Typically, US officials favour the language of diplomatic threats when they talk to Sudan, but Sen Kerry instead spoke of the rewards on offer if Khartoum did not obstruct the referendum, our correspondent says.
He said he had received a written "resolution vowing in concrete language to abide by the outcome of the referendum, whatever it is, and pledging its co-operation with its neighbours to the south".
If the government kept its word, the US would be able to forge a "new relationship" with Sudan, Sen Kerry added.
"That will have a profound effect on the ways in which the Obama administration and the Congress of the United States can then respond, in terms of our economic relationship and other relationships," he told reporters.
"Our goal is to see a peaceful Sudan, one with which we can have a normal relationship and, indeed, a long-term, growing relationship."