The council said Monday it was standing behind peace deals reached last year in Ethiopia between South Sudan and Sudan.
South Sudan in 2011 became an independent country under the terms of a peace deal ending civil war in the region. Border conflicts, ethnic fighting and disputes over oil have threatened the fragile peace.
The council said there would be "serious implications" if either side failed to live up to its commitments to peace. The Ethiopian deal was meant to address simmering issues from the peace accord ensuring South Sudan's independence.
"Two years on since the independence of South Sudan, the European Union remains convinced that Sudan and South Sudan must coexist peacefully as two viable states," a council statement said.
The EU said it was "deeply concerned" by simmering conflict in Sudan's troubled region of Darfur, but expressed similar frustration with ongoing national security challenges in Jonglei, South Sudan's largest state.
"The EU stands ready, together with the international community, to support Sudan and South Sudan's efforts toward national reconciliation and inclusive national dialogue, and to cooperate with both countries in areas of mutual interest," it said.