More than 8,000 people have fled violence in Sudan's South Kordofan state to South Sudan and more are expected to arrive, the UNHCR warned on Friday.

"These are the first refugees to reach post-independence South Sudan and we expect more arrivals amid persistent reports of aerial bombing in Southern Kordofan," the UN High Commissioner for Refugees said in a statement.

The arrivals are mostly refugees from the Nuba Mountains region, said the UNHCR, noting that arrivals have surged last week to about 500 a day compared to 100 a day in August.

Many of the displaced had walked for several days to arrive in South Sudan.

A lack of airstrips and roads is severely hampering aid access, said the agency, which added that it is developing a camp which would have health, school, clean water and sanitation facilities.

Fighting has raged in the ethnically divided border state of South Kordofan since early June, between the Sudanese army and Nuba militiamen who fought with the SPLA, the former rebel army of the south, during a decades-long civil war with Khartoum.