JUBA, 03 August 2012 [BBC]- Mrs Clinton is the highest-ranking US official to visit South Sudan since it gained independence last July.
A UN deadline for the nations to resolve disputes over their border and oil transit fees passed on Thursday.
South Sudan is the second stop of Mrs Clinton's seven-country African tour.
Arriving from Senegal via the Ugandan capital Kampala, she will spend several hours in South Sudan's capital, Juba, where she will hold talks with President Salva Kiir before returning to Uganda later on Friday.
While affirming strong US support for South Sudan, Mrs Clinton will voice concern about a "lack of movement" in talks between the two Sudans, according to an unnamed US official.
Exports suspended
Her visit comes nearly a month after South Sudanese celebrated the first anniversary of independence, which was brought about by a 2005 peace accord.
When South Sudan seceded from Sudan on 9 July 2011, it took about three-quarters of its oil reserves with it, but all the pipelines used to export the oil run through the former north.
The dispute over how much South Sudan pays to use these remains unresolved, leading Juba to suspend oil exports completely in January.
The move has caused widespread economic hardship in both countries, whose budgets depend heavily on oil income.
The two countries came close to all-out war in April, when South Sudanese troops briefly occupied the disputed oil-rich border area of Heglig.
Negotiations between the two countries in the Ethiopian capital, Addis Ababa, aimed at resolving all outstanding issues, have so far produced no agreement.
On her return to Kampala later on Friday, Mrs Clinton is expected to press Ugandan officials to step up the hunt for the leader of the rebel Lord's Resistance Army, Joseph Kony.