Up to 13,000 South Sudanese have sought refuge at United Nations compounds in Juba, the UN said on Tuesday.
Speaking to South Sudan President Salva Kiir on telephone, UN Secretary General Ban Ki-moon urged President Kiir to offer to hold talks with opponents of his government and to "guarantee the protection of all civilians regardless of their ethnicities," a spokesman for Mr Ban told reporters.
The secretary-general added that "he was counting on the president to exercise real leadership at this critical moment," the spokesman added.
Mr Ban also called on President Kiir to instil discipline in the ranks of the SPLA to stop the fighting among them.
Reports from Juba say more than 63 South Sudanese soldiers have been killed in fighting that pits loyalists to President Kiir against supporters of former Vice President Riek Machar.
UN officials in Juba are warning of an ethnic dimension to the clashes. President Kiir is a member of the Dinka group while Mr Machar belongs to the Nuer community.