The ultimatum was issued by Sudan's minister of international cooperation at a news conference, the Sudan Tribune reported Tuesday.
"We have informed the U.S. deputy chief of mission in Sudan, Dennis Hankins, that unless they quit their propaganda of famine in the three areas, we will expel them," said Ishraqa Said Mahmoud.
Last month, the United Nations Security Council issued a U.S.-backed statement expressing "growing alarm" over rising levels of malnutrition and food insecurity in the states of South Kordofan and Blue Nile.
Khartoum has been facing international pressure to let international aid groups operate in Sudan's border states where fighting between government and rebel forces has displaced more than 417,000 people.
The threat to expel the United States diplomatic mission comes just days after Sudanese President Omar al-Bashir criticized U.S. policy towards his country.