Aid to the Church in Need and its Catholic partner in the region, that cannot be named for security reasons, said that renewed violence in the capital Juba is causing enormous suffering.
The unnamed charity said: "The way the various governments all over the world are panicking and acting shows that they fear that something terrible is still to happen.
"One can even hear that 'the worst is still to come!'"
Fighting began as South Sudan celebrated five years of independence earlier in the month.
Conflict is mainly between forces loyal to President Salva Kiir Mayardit and those faithful to the vice-president James Wani Igga.
South Sudan became an independent country in 2011 and has a significant Christian population.
The international community is concerned that continued fighting might result in the country descending into another civil war just months after a ceasefire was agreed.
A spokesperson from the unnamed charity went on: "Let's pray that the nightmare in Juba and all around the country is soon coming to an end.
"People just cannot stand this hell any longer. I am seeing people leaving Juba in big numbers, mostly to Uganda, whenever they find a possibility and when they can afford it."
Through the church, 1,385 registered families - which numbered 7,183 displaced people - were able to receive support at St Paul's Seminary campus in Juba.
More than 300 people have been killed and the death toll is expected to rise.
The leader of Catholics all over the world, Pope Francis, has sent a special envoy to South Sudan to urge for an end to violence in the country.
He has sent Cardinal Peter Turkson, president of the Pontifical Council for Justice and Peace to Juba to help establish dialogue and trust between the warring parties.
He has taken a letter from the Pope with him, for President Salva Kiir and one for Vice President Riek Machar who are historic enemies and represent the different ethnic groups.
Cardinal Peter Turkson told Vatican Radio: "To put it mildly: the situation is tough."
He went on: "A lot of the women and children and even boys have sought refuge in Churches and in schools - and that is where they live - and the priests and brothers and nuns try to take care of them as best as they can."
