Thousands of people are feared dead, U.N. officials said, while close to 200,000 civilians have been forced to flee their homes - many seeking refuge with badly overstretched U.N. peacekeepers.
Jacob Kurtzer, a representative of the International Committee of the Red Cross, told Al Jazeera that refugees need immediate help.
The U.N. has said it will do everything it can to prevent further "terrible acts of violence" in South Sudan.
"We have seen terrible acts of violence in the past two weeks, there has been killings and brutality, grave human rights violations and atrocities committed," Hilde Johnson, U.N. special representative to South Sudan, told Al Jazeera.
The conflict has been marked by an apparent surge in ethnic violence pitting members of Kiir's Dinka tribe against Machar's Nuer community.
The U.N. Mission in South Sudan (UNMISS) said "atrocities are continuing to occur" across the country despite efforts to negotiate a ceasefire.
"UNMISS is gravely concerned about mounting evidence of gross violations of international human rights law that have occurred in South Sudan during the past 15 days," it said in a statement, reporting "extra-judicial killings of civilians and captured soldiers" and the "discovery of large numbers of bodies" in Juba, Bor and Malakal, the main town in oil-producing Upper Nile state.
UNMISS has said it is "actively collecting information" on the atrocities to be used for future official investigations.
U.N. Secretary-General Ban Ki-moon has already given warning that senior South Sudanese figures "will be held personally accountable" for any crimes against humanity.
Johnson, the U.N. special representative, has said there is evidence that South Sudanese citizens are being targeted "on ethnic grounds".
"This can lead to a perpetual cycle of violence that can destroy the fabric of the new nation," she said.
"We need to do everything possible to prevent such a cycle of violence between communities of South Sudan."
However South Sudan political analyst Matthew LeRiche told Al Jazeera the fighting is "very much a political struggle" rather than an ethnic conflict.
He noted that Kiir and Machar belonged to the same government and the same party, until they split due to political differences.
Published under an agreement with Al Jazeera.