The 21-year war, which broadly pitted the Islamic northern government against the mainly Christian and animist south, killed more than 2 million people, most from famine and disease.
Sumbeiywo, whose job now is to ensure implementation of the accord, said since peace was signed, southern Sudan "has been very easily forgotten." Foreign attention was more focused on conflict in the western region of Darfur, he added.
Infrastructure remains negligible in the vast south -- the size of half of western Europe -- and the creation of institutions to help former southern rebels join Sudan's new power-sharing government is going slowly.
Money pledged in January needed to be released quickly, and there was a lack of foreign experts on the ground, he said.
"My plea to the international community is please do what it takes to support the peace agreement, irrespective of what is happening in Darfur," he told Reuters. "Going back to war is probably the worst thing that can ever happen to the Sudanese."
Despite some delays in implementation of the accord, including formal constitution of Sudan's new government, the end to what was then Africa's longest-running conflict is generally viewed as a success story for the continent.
"If we do it well, then we can do it in Congo, in Somalia, in many other places," Sumbeiywo said, listing two nations whose names have become synonymous with chaos and conflict.
"GARANG'S BLOOD BONDS SOUTH"
The Kenyan said delays in the Sudan deal's implementation were understandable given logistical difficulties in Africa's largest nation and the death of former southern rebel leader John Garang who had taken Sudan's vice-presidency in the deal.
Garang died in a July helicopter crash.
Sumbeiywo said, however, the ruling National Congress Party and its foe-turned-partner the Southern People's Liberation Movement (SPLM) now needed to get their act together fast.
"If it (the new government) is not implemented by the end of this month, somebody should raise the red or the yellow card to say 'you are too slow'," he said.
He disagreed with some analysts' view that the NCP was dragging its feet over relinquishing power to the SPLM. "If they were reluctant, they would have been reluctant in swearing in General Salva Kiir," he said of Garang's replacement.
He also expressed confidence the sometimes fractious SPLM leadership would stick together. "The blood of Dr. John Garang is bonding them very well and will continue to do so. It is bonding all southerners, not just the SPLM."
Sporadic violence in the south was due to local disputes over resources, not any threat of a return to war, Sumbeiywo added. "Violence in Africa never ceases, especially with things like cattle-rustling. But we have not seen military operations."