Sudan's President Omar Hassan al-Bashir said Sudan wants a lasting peace with South Sudan but Juba needs to end support for rebels in Sudan's border land, state news agency SUNA said on Saturday.
Oil, security and frontier disputes ignited border clashes last month and for a while raised fears of full-blown war in one of Africa's most significant oil regions.
South Sudan became independent in July under a 2005 peace agreement with Khartoum that ended decades of civil war. But the neighbours failed to mark the joint border and agree how much landlocked South should pay to export its oil through Sudan.
Bashir met late on Saturday former South African President Thabo Mbeki, who is trying to bring both sides back to the negotiation table at the African Union. Mbeki is due to fly to the southern capital Juba on Friday.
Bashir told Mbeki Sudan was committed to a lasting peace but South Sudan needed to end its support for rebels in the border states of South Kordofan and Blue Nile and withdraw all its forces from there, SUNA said after the meeting.
South Sudan denies it supports rebels of the Sudan People's Liberation Movement-North (SPLM-N) which is fighting the Sudanese army in both states, which border South Sudan.
Bashir also told Mbeki that to achieve peace South Sudan should not attack Sudan again. Last month, South Sudan's army took the disputed border oil field of Heglig before announcing a withdrawal following pressure from the U.N. Security Council.