Western powers fear the violence could spiral out of control and lead to a civil war split along ethnic lines in the world's newest state, and the U.N. Security Council on Tuesday agreed to almost double the number of peacekeepers there.
"Innocent people have been wantonly killed. People are targeting others because of their tribal affiliation. This is unacceptable," Kiir said, according to an official Twitter account of South Sudan's government.
"These atrocities recurring by now have to cease immediately," Kiir added.
The violence erupted in the capital Juba on Dec. 15 and has quickly spread, dividing the landlocked country of 10.8 million along ethnic lines of Nuer and Dinka.
Western powers and east African states, keen to prevent more chaos in a fragile region, have tried to mediate between Kiir, a Dinka, and rebel leader Riek Machar, a Nuer, who was vice president until Kiir sacked him in July.
European Union foreign policy chief Catherine Ashton is sending an envoy to the country, the European Commission said on Wednesday. A South Sudan government official said Ethiopian Prime Minister Hailemariam Desalegn and Kenyan President Uhuru Kenyatta would arrive in Juba on Thursday morning to help mediate as well.
Despite African Union calls for a Christmas Day ceasefire, rebels and government troops on Wednesday clashed in Malakal, capital of the major oil state of Upper Nile.
"In Malakal, rebel forces are on one side, and government troops on another. Fighting is still taking place," Army spokesman Philip Aguer told Reuters on Wednesday.
A United Nations human rights group on Tuesday found a mass grave containing 75 bodies in a rebel-held town.
Kiir and Machar have both said their dispute is political, not tribal. But many of the 45,000 civilians seeking refuge inside U.N. bases across the country say they have been targeted based on their ethnicity.
"It's definitely not a good Christmas here in the abyss of war," said Chan Awol, a 30-year old civil servant whose family has scattered across South Sudan after the fighting started.
"Nobody wants to go back to the days when there were no schools, no hospitals and no roads. Above all, no South Sudanese wants to be a refugee again."
U.N. Secretary-General Ban Ki-moon on Christmas Day delivered a radio message to South Sudanese people, saying the U.N. will stand with them during the country's most difficult period since gaining independence from Sudan in 2011.
"We are strengthening the United Nations presence and will do our best to stop the violence and help you build a better future for all," Ban said.
Machar told Reuters on Monday that he was willing to negotiate with Kiir but only if his detained political allies are freed, something the government swiftly rejected.
Army spokesman Aguer said government troops will within a few days attack the rebel-held town of Bentiu, capital of Unity state, which also produces oil.
South Sudan's Petroleum Minister Stephen Dhieu Dau said on Tuesday that oil production, which accounts for 98 percent of government revenue, had fallen by 45,000 barrels per day to 200,000 bpd after Unity state oilfields shut down.
Government officials say production in the Upper Nile area is unaffected as the oil fields are far away from Malakal.