Tens of thousands of people are fleeing from intense fighting along the undefined border region between northern and southern Sudan, with humanitarian officials warning the violence is getting worse.

The United Nations said Friday conditions have deteriorated rapidly in the north's South Kordofan state, where civilians are getting caught between the north's Sudanese Armed Forces and the south's Sudan People's Liberation Army .

U.N. officials in Geneva said an estimated 40,000 people – two-thirds of the population – have fled from the state capital of Kadugli. They said roadblocks have also been set up, preventing humanitarian aid from getting through. They also said there are an increasing number of reports of civilians being shot and killed when they return to their homes for food and other necessities.

Meanwhile, south Sudan is accusing the north of carrying out bombing runs in the south's Unity state and said at least three people were killed in the attacks Friday.

The United States Friday condemned the violence in the region as “reprehensible.” A White House spokesman said accounts of military forces executing local authorities, political rivals, and medical personnel could constitute war crimes. He called on Sudan's government to “consider carefully” the consequences of its current actions which he said could put the country on a path toward deeper international isolation.

South Sudan voted to secede from the north in January and will officially declare independence next month.

The vote was the culmination of a 2005 peace deal between the warring sides but many issues, including a defined border and the fate of the oil-rich Abyei region, have never been decided.

On Friday, U.N. Independent Expert Mohamed Chande Othman called on both the north and south to adhere to the peace deal and stop the situation from unraveling further.

Othman also raised concerns about growing allegation of killings, rape and other human rights violation in Abyei after Sudanese forces occupied the area.

The U.N. has previously called on Khartoum to withdraw its forces.