South Sudan's leader Salva Kiir has said he will not lead his people back into conflict with the north over the disputed region of Abyei.
The region, seized by northern troops at the weekend, is also claimed by South Sudan, which is due to become independent from the north in July.
"We will not go back to war, it will not happen," Mr Kiir said in his first public statement since trouble began.
Analysts fear the dispute could reignite the north-south conflict.
A peace deal in 2005 ended 22 years of civil war in which some 1.5 million people died.
The status of Abyei was left undecided and a referendum, due last January, on whether the area should be part of the north or south has been postponed indefinitely.
In a national address, Mr Kiir said the south had "fought enough" and that it was time for peace.
He described the north's invasion of Abyei as an over-reaction, and said the area would eventually be reclaimed by the south.
Sudan's President Omar al-Bashir has refused to withdraw his troops from the region, despite UN condemnation of the move.
Earlier, a southern minister in the national government resigned, saying "war crimes" had been committed in the disputed Abyei region.
The Satellite Sentinel Project has released satellite images of burnt huts and says they provide evidence of war crimes.
The project's spokesman Jonathan Hutson said other troop movements in the north were also a cause for concern.
"Satellite Sentinel Project has identified Sudan armed forces, those of the northern armies, massing near the contested border area of Abyei with heavy armour and artillery and tanks at a place called El Obeid - there's a barracks there," he told the BBC's World Today programme.
"They could reach Sudan's north-south border or Abyei town in less than a day without refuelling."
Aid workers say some 40,000 people have fled the fighting around Abyei - mostly southerners, heading further south.
"Tens of thousands have been displaced - the villages that they've left behind have been systematically razed," Mr Huston said.
David Deng Bol, manager of Mayardit FM radio station in Turalei, about 75km (45 miles) south of Abyei, told the BBC more than 25,000 people had arrived in that area in the last few days.
Many were camping under trees and in the rush to leave some families had been split up and children were missing, he said.
"The situation of the IDPs [internally displaced people] is very very bad. They sleep outside being affected by the rain, the places are cold, there's no food, no water or no medication," he told the BBC's Focus on Africa programme.
Meanwhile, the UN has said it believes militiamen from the Misseriya ethnic group were responsible for shooting at one of its helicopters on Wednesday.
The Misseriya are northern nomads and one of two groups to claim Abyei, along with the southern Dinka Ngok people.
They were armed by Khartoum and used to attack the south during the civil war.
Reports suggest many Misseriya have arrived in Abyei town since the northern armed forces took control of it on Saturday, accusations denied by one nomad leader as "nonsense".
Under the 2005 peace agreement, Abyei was granted special status and a joint administration was set up in 2008 to run the area until a referendum decided its fate.