The UN High Commissioner for Refugees says 37,890 people have been forced to flee the country to Uganda following the recent clashes between the SPLA and Opposition forces in Juba.
It says they are coming from the Eastern Equatoria region, as well as Juba and other areas of the country.
The agency says there have been more refugees arriving in Uganda since the incident than the entire first six months of 2016.
In a statement, the UNHCR says on the 25th of this month alone, 2,442 were received in Uganda.
It says daily arrivals were at the average of1, 500 ten days ago, but the number has risen to over 4,000 in the past week.
The UNHCR says 90% of the arrivals are women and children. It says agency says the situation is extremely worrying.
The agency says the huge number of refugees is putting serious pressure on the capacity of collection points, and transit and reception centres, which are too small for the growing number of arrivals.
It says 1,213 crossed at the Elugu Border Point in Amuru, 247 in Moyo, 57 in Lamwo, and 370 in Oraba. The agency says other 555 were received in Kiryandongo Settlement.
Some 300 people are reported to have been killed in the recent clashes in Juba.