There are fears that violence in the border state could unsettle South Sudan's secession on July 9 and reverse the peace process.
More than 98 per cent of southerners voted to secede during a surprisingly peaceful referendum in January, but the contested areas of South Kordofan, Abyei and Blue Nile have seen acts of aggression by northern Sudanese forces.
These include the invasion of Abyei last month, which has led to the displacement of some 100,000 people in the oil-rich area, according to UN estimates.
Fighting in Kadugli, the state capital of South Kordofan, has caused up to 40,000 people to flee their homes.
The Archbishop warned of "another Darfur" unless the international community helped to safeguard citizens and humanitarian access.
He expressed his solidarity with the Sudan Ecumenical Forum and Council of Churches.
"We deplore the mounting level of aggression and bloodshed in South Kordofan State and the indiscriminate violence on the part of government troops against civilians," he said.
The Archbishop said that the new Anglican cathedral had been burned down and warned that UN personnel in Kadugli were "unable to protect civilians".
"The city has been overrun by the army and heavy force is being used by government troops to subdue militias in the area, with dire results for local people," he said.
"Many brutal killings are being reported.
"This violence is a major threat to the stability of Sudan just as the new state of South Sudan is coming into being.
"The humanitarian challenge is already great, and the risk of another Darfur situation, with civilian populations at the mercy of government-supported terror, is a real one."
The Archbishop said that international awareness of the situation was "essential" and called upon the UN Security Council, the EU, Arab League and African Union to cooperate in guaranteeing humanitarian access and safety for citizens.
He added: "We hope that our own government, which has declared its commitment to a peaceful future for Sudan, will play an important part in this."