The UN Refugee Agency says Uganda’s Lamwo district has received over 6,000 South Sudanese since violence erupted in Pajok in Imatong State on Monday.
The SPLA said 18 people were killed in the clashes with an armed group in the area.
The deputy SPLA spokesperson, Colonel Santo Domic, said the army was responding to the attack.
The UNHCR says the refugees have reported that they witnessed killing of some of their loved ones during the fighting, including the vulnerable.
The agency says the families fled in different directions.
The witnesses say many people are still in the bush trying to find their way to Uganda, while homes and properties were looted and burned.
UNHCR says they also say main roads out of the town are reportedly blocked by armed groups.
In a statement, UNHCR says the refugees are in dire need of immediate humanitarian assistance including food, shelter, water and medical care.
It says around 4,000 refugees immediately fled South Sudan in the after aftermath of the attack on Pajok town and 2,000 later followed.
It says Pajok has an estimated population of up to 50,000.
Uganda currently hosts more than 832,000 refugees from South Sudan. Some 192,000 have arrived in 2017.