Fighting that broke out in the capital, Juba, in July is responsible for the latest surge in those fleeing, it says.
More than 1.6 million people are also displaced within South Sudan, meaning about 20% of the population have been made homeless since December 2013.
A fragile peace deal signed last year is on the brink of collapse.
"The violence in July came as a major setback to peace efforts in South Sudan," the UNHCR spokesman Leo Dobbs said in a statement.
The UN says more than 185,000 people have fled South Sudan since July.
"The fighting has shattered hopes for a real breakthrough and triggered new waves of displacement and suffering, while humanitarian organisations are finding it very difficult for logistical, security and funding reasons to provide urgent protection and assistance to the hundreds of thousands in need," Mr Dobbs said.
Many of the refugees arriving in Uganda, which hosts the most South Sudanese, are "exhausted after days walking in the bush and going without food or water. Many children have lost one or both of their parents", the UNHCR says.
A fall-out between President Salva Kiir and former Vice-President Machar - the most powerful members of their respective Dinka and Nuer ethnic groups - led to the civil war which erupted in December 2013.
They only agreed to settle their differences under intense international pressure, signing a peace deal in August 2015 - and Mr Machar returned to Juba as vice-president in a unity government in April.
But battles then broke out between his bodyguards and presidential guards three months later, prompting him to flee.
Another member of his party has been appointed as vice-president, a move Mr Machar does not recognise.
Earlier this week, a report funded by George Clooney accused both Mr Kiir and Mr Machar, as well as their officials, of personally profiting from the war. Both men have denied the allegations.
The UN wants to deploy a 4,000-strong regional protection force for Juba which would have a more robust mandate than the 12,000 UN soldiers already in the country, however the mandate and size of the force still have to be agreed.
South Sudan refugees:
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