But Sudan's UN envoy said there could only be peace between the neighbouring states when the South ends its support for rebel groups operating in Sudan.
South Sudan's Foreign Minister Deng Alor Kuol gave his commitment after the UN Security Council passed a resolution which gave the two countries 48 hours to halt hostilities and warned of possible sanctions if they fail to heed the international call.
The minister told the council the South's government "formally appreciates the adoption of the resolution and state our solemn commitment to comply with its mandated provisions".
"My government is already committed to the cessation of hostilities and resumption of negotiations under the auspices of the African Union," Kuol added.
The minister appealed to the United Nations "to urgently mobilise humanitarian assistance for the population affected by Sudan's continuous aerial bombardments and ground incursions" into the South.
Tensions between Sudan and South Sudan have spread along their uncharted border since the two countries split in July last year. Each accuses the other of aiding rebels operating across the border. Sudan has also been accused of staging air raids in the South.
Sudan's UN ambassador Daffa-Alla Elhag Ali Osman gave no formal commitment to the council over the resolution. He said responsibility for peace efforts must stay with the African Union.
"Peace between the two republics, Sudan and South Sudan, will only be achieved by halting all forms of support and sheltering proxy rebel and armed groups espoused by South Sudan," Osman told the council.
He said the council should have set a deadline for the end of support for rebels and added that it was "notable" that "the resolution has disregarded the continuous aggression by South Sudan against Sudan."
"It is our right though to use all military means inside our territory - I reiterate inside our territory - to rebuff" aggression from the South, the envoy said.