South Sudan's refugee exodus continues unabated with up to 2,500 people crossing into Uganda daily, the United Nations refugee agency (UNHCR) reported.

Ceasefire talks between the South Sudan government and rebels are struggling to gain traction in Ethiopian capital Addis Ababa.

As of Tuesday some 23,546 South Sudanese refugees had arrived in Uganda.

"They are now crossing at a rate of up to 2,500 people a day," UNHCR spokesperson Melissa Fleming told a news briefing in Geneva.

These new arrivals come at a time when UNHCR's Uganda office is trying to cope with a continuing influx of refugees from the Democratic Republic of the Congo (DRC).

"We still have 8,000 new Congolese arrivals at three reception centres in western Uganda, so our staff and our supplies are stretched," Ms. Fleming said.

Smaller but growing numbers of South Sudanese refugees are also fleeing to other neighbouring countries.

More than 5,300 refugees have been registered in Ethiopia – though the number is likely higher as the remote border area is hard to access.

In north-west Kenya's Kakuma Refugee Camp, where as many as 300 South Sudanese are now arriving daily, UNHCR staff registered 3,173 new arrivals by Sunday evening.

The situation in Sudan remains less clear. Several thousand South Sudanese may have crossed the border, but with many groups, including nomads and rebels, active in the area, it is difficult to know exactly how many are refugees, Ms Fleming said.

Representatives of South Sudan President Salva Kiir and sacked deputy Riek Machar are meeting in Addis Ababa, Ethiopia, in talks mediated by regional bloc the Intergovernmental Authority on Development (IGAD), with an immediate ceasefire at the top of the agenda.

Inside South Sudan, UNHCR is operating with a reduced staff of 200 people because of fighting and insecurity throughout much of the country, but it continues to supply services to some 230,000 existing refugees at 10 camps in South Sudan.

"We have also been taking on increased responsibilities for the 57,000 civilians taking refuge in 10 UN compounds throughout the country,” Ms Fleming said

"We are helping lead efforts to protect especially vulnerable people like women and children. And we have brought in experts in areas such as site planning and camp management."