Mustafa made the call in a press statement issued following his meeting with visiting US Secretary of State Condoleeza Rice.
Mustafa said he had urged the US to review its sanctions imposed on Sudan as "no longer reasons for them after the signature of the southern Sudan peace agreement and the ongoing improvement in the situations of Darfur."
Ismail said his meeting with Rice detailed the stages of the implementation of the south Sudan peace agreement and the steps towards a national unity government in Sudan.
The two sides focused on the security and humanitarian situations in Darfur and the role played by the African Union (AU) as well as the need for the US to support the expanding of the AU mandate in Darfur.
Ismail described Rice's visit to Sudan as important, which sends clear signals that the relations between Sudan and the US have reached important stage, adding that the two sides were committed to work together to restore peace in Sudan.
He said that Rice's visit has given her an opportunity to see for herself the situations in Sudan, especially that it was her first visit to Sudan since she took office as the US secretary of state.
Ismail noted that Rice expressed her optimism that the mutual relations will improve in the future and promised to work for that, said Ismail.
Rice confirmed the normalization of bilateral relations would go along with the implementation of the peace agreement in the south and the improvement of the situations in Darfur, he added.
The United States recalled its ambassador to Sudan Tim Carney in 1997 after Washington imposed sanctions on the country, accusing it of supporting terrorism.
Ties between the two countries have remained frosty since then. Currently, the top US representative in Sudan is a charge d'affaires.
Following a long period of tension, the US-Sudan relations have thawed recently, with a joint committee established to discuss ways of normalizing ties.
Rice arrived here early on Thursday on a one-day visit to Sudan.