The agency said the facilities were inadequate for the more than 6,500 people scattered in 12 villages along the border who are being hosted by the local communities.
"It is very difficult for us to provide assistance to the refugees at the border, where the security situation is unstable and people are scattered in various villages," Stefano Severe, UNHCR representative in Uganda, said.
He said the agency had established a permanent presence in Kisoro area of western Uganda to better monitor and respond to the emergency, which follows weeks of fighting in North Kivu Province between Congolese troops and those loyal to renegade army commander Laurent Nkunda.
"Our first step will be to start an information and sensitisation campaign to inform refugees about the protection and assistance that they will be offered in Nakivale refugee settlement, if they take the option of moving there with our help," Severe said.
Refugees have continued to flee into Uganda, with at least 600 arriving on 31 October in Ishasha, Kanungu district. Some of the refugees have indicated to UNHCR that they would like to be directly relocated to Nakivale refugee settlement.
Most of the Congolese who arrived in the last three days fled from Rugarama village, 17km from the Ugandan border, and walked more than 20 hours to reach Uganda through Busanza border point in Kisoro.
"They reported that their village had been taken over by Nkunda's rebels and their lives were in danger," Roberta Russo, the UNHCR spokeswoman, told IRIN.
At least 8,500 refugees have entered Uganda since August.
Russo said although the condition of the 6,500 Congolese settled along the border in Kisoro was satisfactory, the situation could rapidly deteriorate if the number of newcomers increased and the refugees decided to remain scattered in villages along the border.
"Food supplies, health, water and sanitation facilities are not able to adequately assist an additional population of 6,500 people," she said.
UNHCR says a small transit centre and a regular system of transportation from Kisoro to Nakivale would be set up for the refugees who were willing to move.
"Should the influx of refugees from DRC continue and reach over 20,000 people, we might establish a reception centre in Nyakabanda, 15km from the border, where, with the help of the local and central governments, WFP [World Food Programme], UNICEF [UN Children's Fund] and other NGO partners, the refugees will have access to clean water, sanitation facilities, shelter and food," Severe said in a statement.
Uganda presently hosts 146,407 refugees, including 48,606 Congolese.