An estimated 5,000 refugees have crossed South Sudan's southern border and arrived near the Congolese town of Ingbokolo, according to local village chiefs.
In addition, some 8,000 South Sudanese are believed to be displaced within their country near the town of Yei, UNHCR spokesman Babar Baloch a press conference in Geneva.
The people who reached Congo over the weekend on foot are mostly women, children and elderly people.
"Many have been suffering from trauma from having witnessed violent incidents, including armed men reportedly murdering and raping civilians and looting villages," Baloch said.
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Armed clashes broke out on January 19 between the armed forces and the National Salvation Front rebels in Central Equatoria State.
More than 70 rebel groups are active in South Sudan, according to Baloch.
The fighting had initially subsided after major conflict parties concluded a peace agreement in September.
South Sudan, founded in 2011, is the world's youngest country.
In 2013, a split between President Salva Kiir and his former deputy Riek Machar triggered a civil war that has led to tens of thousands of deaths and the displacement of 2.5 million people.