More than 20 years of civil war in southern Sudan killed more than 2 million people died, mainly from war-induced famine and disease, and forced at least twice as many to flee their homes.
A peace deal was signed in December between the main southern Sudanese rebel group and the Sudanese government.
But UNHCR reported last week that since the peace deal was signed, more than 8,000 Sudanese have crossed the border into Uganda.
The new refugees complained that ethnic tensions were on the rise, the Sudan People's Liberation Army was forcing young men to join their ranks, food aid had been cut off to some areas and a Ugandan rebel group was also attacking Sudanese civilians, UNHCR said.
The agency added it may be more difficult than expected to persuade Sudanese already in Uganda to return home.
The refugee agency had planned to repatriate Sudanese from Uganda beginning in August.