Thousands of people have fled tribal killings in the eastern Democratic Republic of Congo (DRC) in the past week.
Many are now camped in the western Ugandan district of Bundibugyo.
"Many people have come in and they have already exerted pressure on the resources here," Bundibugyo Resident District Commissioner Erasto Gubaare said on Friday.
Ugandan soldiers sing and dance as they
prepare to leave the eastern Congo town
The UN World Food Programme (WFP)confirmed the influx of refugees, but said it had not compiled figures for those entering Uganda, mainly through Rwebisengo border areas.
WFP Deputy Resident Director Edward Kellon said the UN High Commission for Refugees (UNHCR) had not contacted them for any assistance, but pointed out that a WFP team was already in the affected area.
Gubaare said most of the refugees were women, children and elderly Hema tribespeople, who have alleged that their long-time rivals the Lendu and their allies the Ngitis were killing them on sight.
Appealing for help from the UNHCR and other agencies, Gubaare said 1,750 Congolese had entered the Kanara sub-county of Kyenjojo district. Another 7,159 were in Ntoroko sub-county, while figures for Rwebisengo, where 3,300 refugees arrived last week, had not yet been compiled.
But the UNHCR maintained that it would only intervene if the refugees moved to facilities set up for them in nearby Kyenjojo district.
"We shall not provide them with international protection, unless they move to designated refugee areas," UNHCR spokeswoman Bushila Malik said in Kampala.
At least 60 people, mostly women and children, were killed in a massacre in eastern DRC last weekend. They blamed it on Lendu militiamen, who are alleged to have ambushed them near River Semliki as they walked towards the Ugandan border.
An official in northwest Uganda, Peter Odok W'ocheing, said over 10,000 people were also camped inside DRC waiting to cross the border.
"UN peacekeepers should be sent to these areas to protect these people," he said.
The Ugandan army started withdrawing thousands of troops from DRC's volatile Ituri region a week ago and has since flown out over 1,600 soldiers from the main town of Bunia, while the majority are walking back home in an exercise that will take up to three weeks.
Ugandan troops withdraw
The Hema and Lendu tribes have a long-standing and deep-rooted rivalry, mainly over land ownership and mineral resources.
The Lendu live primarily from their crops while the wealthier Hema rely on cattle raising and cultivation - distinctions mirroring the Hutu and Tutsi of neighbouring Rwanda, which saw 800,000 slaughtered in a 1994 genocide.
The traditional rivalry has degenerated over the last five years into a bloody killing spree as the tribal militias, once armed with clubs and machetes, were given guns and other weapons by rival rebel armies and their allies from Uganda and Rwanda.