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More than one million people from South Sudan have been forced to flee to neighbouring Uganda alone, with another million seeking refuge from the brutal civil war elsewhere in the region, the UN's refugee agency said on Thursday.

An average of 1,800 South Sudanese have arrived in Uganda every single day over the past year, the UNCHR said, noting additional funds were desperately needed to help the refugees flooding into the neighbouring country.

More than 85 percent of the South Sudanese refugees in Uganda are women or children and youths under the age of 18 who fled "barbaric violence" at home.

"Recent arrivals continue to speak of barbaric violence, with armed groups reportedly burning down houses with civilians inside, people being killed in front of family members, sexual assaults of women and girls, and kidnapping of boys for forced conscription," it said in a statement.

The UN agency warned that "with refugees still arriving in their thousands, the amount of aid we are able to deliver is increasingly falling short".

UNHCR estimates it will need $674 million (576 million euros) this year alone to help the refugees in Uganda, but lamented that so far it had received just a fifth of that amount.

"The funding shortfall in Uganda is now significantly impacting the abilities to deliver life-saving aid and key basic services," it said.

In June, the UN's World Food Programme had to slash food rations for refugees in the country, while doctors, nurses and medicines are in short supply, it said.

Schooling has also been affected, with class sizes often exceeding 200 pupils, teachers forced to hold lessons outdoors, and many refugee children dropping out because of long distances and other difficulties accessing schools.

South Sudan, the world's youngest nation, descended into civil war in December 2013, just two years after it split from the north.

Thousands of people have been killed and millions displaced by the violence, which briefly plunged part of the country into famine earlier this year.

In addition to the one million South Sudanese refugees in Uganda, at least another million have fled to Sudan, Ethiopia, Kenya, the Democratic Republic of Congo and the Central African Republic, according to UN numbers.

A further two million people are estimated to have fled their homes and sought refuge elsewhere in the war-ravaged country.

Agencies contributed to this report.