Medical charity Medecins Sans Frontieres (MSF) charity says that in the past three days 25,000 South Sudanese have been displaced by intense fighting around the northern town of Kodok.
MSF said aid organisations have suspended operations due to the insecurity.
The UN says the government launched a new offensive in the area, against Agwelek rebel forces.
Many people in Kodok fled there recently from fighting in other areas.
MSF said the fighting had forced all hospitals in the area to close.
It has been impossible to deliver water to displaced people who are living outside under scorching sun.
Many are making their way by foot to Sudan.
The head of the UN mission in South Sudan, David Shearer, said the conflict had widened in recent weeks.
South Sudan, Africa’s newest country, has had an unhappy six years of independence.
Its leaders fell to fighting, and seem oblivious to the immense suffering of civilians.
Earlier this year, the UN formally declared a famine, a disaster it described as man-made.
.@MSF calls on all warring sides in #Kodok to ensure civilian safety & access to #humanitarian aid #SouthSudan https://t.co/5IKinmDlmt— MSF South Sudan (@MSF_SouthSudan) April 27, 2017
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