However, the Sudanese army denied the SPLA's claim that it had taken part in the fighting.
"We were not involved in these clashes," Sawarmi Khaled Saad, an army spokesman, said.
"If one of the partners in the comprehensive peace agreement (CPA) has such allegations to make about the other, the joint defence council should speak about it."
The Khartoum government signed the CPA with the Sudan People's Liberation Movement (SPLM) in 2005, ending decades of a civil war.
Under the deal, Sudan's oil-producing, semi-autonomous south was allowed to keep the SPLA as a separate army.
Southerners will vote in referendum on whether to break away from the north on January 9, 2011.
Account of events
Al Jazeera's Mohammed Adow, reporting from Khartoum, said: "UN sources have confirmed to us that the attack took place inside Darfur region and it is part of the border and such incidents are frequent."
But he said that it was unclear whose account of events was correct.
"According to the SPLA, the attack was carried out by the [northern] Sudanese armed forces ... in Bahr al-Ghazal state," our correspondent said.
"But the Sudanese forces are saying that the attack was carried out by the SPLA on one of their Arab tribes in Darfur and they had a clash with the militias of this particular tribe."
Aliou, of the Rezeigat tribe, said tensions remained high in the region, which is plagued by fighting between rival ethnic groups, following Friday's clashes.
"There are many members of the Rezeigat tribe who are heading to the site of the clashes in order to help out," he said.
"There are also reinforcements from the south Sudan army coming from three cities Raja, Aweil and Wau."
More than 400 people have been killed across the south in cattle raids and revenge attacks this year, according to the United Nations.
The violence comes as Sudan awaits the results of presidential, parliamentary and regional elections, which the election commission has said could be announced on Monday.
"We hope to be able to announce the result of the national presidential election, or of the presidential election for south Sudan, on Monday, God willing," Al-Hadi Mohammed Ahmed, a senior official with the national election commission (NEC), said.
Omar al-Bashir, the incumbent president, is expected to win re-election easily after most opposition parties boycotted the poll, while his National Congress Party is expected to dominate the federal government.
The SPLM is expected to maintain its hold on the south.