The note, obtained late Monday by The Associated Press, focuses on fighting between government and rebel forces in the Wau Shilluk area of the Upper Nile region that has caused humanitarian organizations to temporarily suspend operations and in Central Equatoria's Kajo Keji county.
It said most of the civilian population approximately 20,400 internally displaced people and local inhabitants - fled Wau Shilluk earlier this month and 30,000 or more have fled three areas of Kajo Keiji since January 22 as a result of fighting, insecurity and fear of reprisals.
A peace deal signed in August 2015 has not stopped the fighting, and clashes last July between supporters of Kiir and Machar set off further violence across South Sudan. The conflict has killed tens of thousands of people and forced 3.1 million to flee their homes.
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The peacekeeping department note, dated Feb. 7, said fighting broke out near Wau Shilluk on Jan. 25 between the rival factions.
It said Kiir's SPLA forces fired multi-barrel rocket launchers, mortars and heavy machine guns across the Nile directly opposite the town of Malakal, targeting positions close to Wau Shilluk.
The UN peacekeeping force relocated 16 aid workers from Wau Shilluk and all emergency services including clinics and water provision stopped February 3 when fighting resumed and local staff fled, the note said. UN humanitarian air flights to Malakal have also been stopped since January 25.
Thousands fled to Uganda, where humanitarian organizations reported the arrival of 28,553 South Sudanese refugees in the last four days of January.