"We have recorded 7,682 arrivals this year of which 1,765 came in during the first three weeks of May and more have come in since then but we have not registered them yet," Roberta Russo, the UNHCR spokeswoman in Kampala, said.
She said many of the refugees recounted that ethnic tensions in southern Sudan were on the rise.
Food aid, she added, had been cut off to some areas, including the internally displaced persons’ camp of Nimule, close to the Ugandan border.
The Uganda rebel group, the Lord's Resistance Army (LRA), which is reportedly based in southern Sudan, was also attacking Sudanese civilians in the areas of Nimule, Torit and Juba, according to Russo.
The rebel group is notorious for its brutality against civilian; frequently maiming, killing and abducting children as fighters, porters or sex slaves.
The northern Ugandan conflict, which began in 1986, has displaced up to 1.4 million people, who live in camps across the region.
Up to 5,000 Sudanese crossed into Uganda between mid-March and May, according to refugee officials in Uganda. Some had arrived at the northwestern district of Moyo. An official in the prime minister's office, who requested anonymity, said the refugees recounted that the rebels attacked with machetes and clubs, looted and set grass-thatched huts ablaze, killing 12 people in one such attack.
There are already 160,000 Sudanese refugees in various settlements in Uganda, and it was hoped that with the peace agreement between the Sudanese government and the Sudan People's Liberation Movement/Army, many would begin to return home. Russo said the latest influx could potentially jeopardise projections that up to 6,000 Sudanese would start voluntary repatriation by the end of the year starting in October.