The fighting that began on Saturday comes as the United Nations and African Union prepare to downsize their peacekeeping mission in Darfur, saying that overall violence there has diminished.
The clashes between the Arab Maaliya and Rizeigat tribes came months after a similar clash left at least nine dead.
The two tribes have a history of violence over land ownership rights and allegations of cattle theft.
"A group of tribesmen from Maaliya were ambushed by members of Rizeigat when they tried to chase thieves who had stolen livestock belonging to Maaliya tribesmen," said Ahmed Nour, a Maaliya leader.
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The chief of the Rizeigat tribe, Mohamed Madibu, told AFP that the two groups also clashed on Sunday.
He said that three Rizeigat were killed in the initial clashes yesterday.
"A group of Maaliya attacked some Rizeigat villages yesterday. There are clashes even today, but we don't have details about casualties," Madibu said.
Khartoum limits international media access to Darfur so it was not possible to independently verify the toll, and Sudanese authorities could not be reached for comment.
The UN and African Union maintain that the Darfur conflict is winding down, and their peacekeeping mission -- among the costliest with a budget of more than $1 billion -- is being trimmed.
The Darfur conflict erupted in 2003 when ethnic minority rebels took up arms against President Omar al-Bashir's Arab- dominated government, accusing it of marginalising the region.
Since then, more than 2.5 million people have been displaced and 300,000 killed, the UN says.