The south's foreign affairs, defence, interior and oil ministers travelled to Khartoum for the talks
South Sudan resumed talks with Sudan on Sunday on a raft of thorny issues, including borders and oil revenues, still outstanding from its 2011 secession.
The south's foreign affairs, defence, interior and oil ministers travelled to Khartoum for the talks, the first since a unity government was formed in Juba last month in a bid to end its devastating civil war.
"There are some difficulties in our relations," South Sudanese Foreign Minister Deng Alor acknowledged at a joint press conference with his Sudanese counterpart Ibrahim Ghandour.
"I delivered a message from our President Salva Kiir to President (Omar) al-Bashir calling for fast resolution of bilateral issues."
The south's independence in 2011 left a raft of issues unresolved, including the status of the Khartoum-occupied border district of Abyei, which had been supposed to hold a plebiscite on its future, and the payments Juba should make for the use of an oil export pipeline through Sudan.
Ghandour said that he would hold further talks with Alor to resolve the issues.
"Sudan's top priority is to build relations with South Sudan given our historical links," he said.
South Sudan's oil production virtually ground to a halt during the civil war that erupted after the dismissal of Vice President Riek Machar in December 2013.
Khartoum is hoping that Machar's return as vice president in a unity government last month will lead to renewed exports through the pipeline to Port Sudan on its Red Sea coast and resumed transit fee payments.
It is also hoping that improved relations will help resolve persistent rebellions on both sides of the border that have sparked a prolonged war of words between the two governments.