The African Union (AU) is calling on Sudan and South Sudan to abide by a plan that will see both parties pull forces out of a disputed border area.
A senior AU official called for hostilities to cease in areas bordering lucrative oil fields.
The United Nations Security Council has also called for an end to aerial bombardments by Sudanese forces.
South Sudan’s President Salva Kiir has said that Sudan has “declared war” on his country.
Recent clashes between Sudan and newly-independent South Sudan over the Heglig oil field and nearby towns have raised fears of a return to war.
Outlining details of a proposed peace deal, AU official Ramtane Lamamra said the African Union would take “appropriate measures” if either country failed to implement the proposed plan.
He said the AU wanted both parties “formally conveying their commitment” to peace within 48 hours.
And he said both Sudanese and South Sudanese forces should pull out of the disputed area of Abyei, near Heglig, within two weeks.
Echoing the demands of the AU, the UN Security Council demanded the cessation of violence and said it will consider what steps to take in order to prevent all-out war.
The Security Council last week discussed the possibility of imposing sanctions on the two countries if the violence did not stop.
Susan Rice, the US Ambassador to the United Nations said: “We strongly condemn Sudan’s incursion into South Sudan and, in particular, its heavy aerial bombardments of civilian areas and infrastructure, and we call for the immediate cessation of hostilities.
“We recognize the right of South Sudan to defend itself and urge South Sudan to exercise maximal restraint in its reaction to Sudan’s attacks.”
In January, South Sudan shut down oil production, which provides 98% of its revenue, after Khartoum impounded South Sudanese oil shipments amid a dispute over transit fees.
South Sudan took most of the former united Sudan’s oil reserves when it seceded in July 2011 but relies on pipelines to seaports in Sudan to export it.
Independence came as part of a peace deal to end two decades of conflict in which some 1.5 million were killed, according to BBC.