Fears of a humanitarian crisis were growing with aid agencies -- themselves forced to restrict their work because of the security situation -- saying there were shortages of food and water.
A fragile ceasefire nevertheless appeared to be holding in the capital Juba for the second day after a sudden flare-up in fighting last week that threatened to drive the world's newest country back into all-out civil war.
But the situation remains precarious, UN peacekeeping chief Herve Ladsous told the Security Council.
"We remain very worried about the potential for the resumption of violence and spill-over into other parts of the country, as we have seen in the past," he said.
Also Read
Thousands of South Sudanese were clamouring to cross the border into Uganda, while Germany and Italy said they were evacuating their nationals and other foreigners.
"There are bodies in the streets, shops have been looted, markets closed, people are queueing for food and families are desperately trying to leave the city," said Peter Walsh, South Sudan country director for charity Save the Children.
In Nimule, the closest border point 200 kilometres (120 miles) to the south of Juba, UN refugee agency officials estimated as many as 20,000 people may be seeking to cross into Uganda.
Those who made it across said South Sudanese soldiers were preventing people from crossing, or relieving them of their possessions before allowing them to pass.
Evacuation flights for foreign nationals were able to leave the international airport in Juba, although commercial flights were not expected to resume until Thursday.
More people ventured on to the streets of the capital, which lies on the banks of the White Nile, but many remained cautious.
"No gunshots today. I have seen no tank, no helicopter," said a resident who did not want to be named. "There are a lot of soldiers and policemen in the streets patrolling.