The Sudanese government in the area of Abyei say that 32 people were killed when armed men attacked the local villages.
The Information Minister of Abyei, Bolis Kuoch, said that more than 20 people were hurt when some men started shooting on Sunday morning.
He said UN peacekeepers stepped in to stop the fighting, but one of them was killed.
There has been a lot of fighting between different groups in Abyei over who gets to use the land and resources.
The area has a lot of oil and is on the border of Sudan and South Sudan. Both countries consider it to be part of their territory because they signed a peace agreement in 2005.
Last week, the UN Security Council agreed to keep its peacekeeping mission in place for another year.
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32 people killed including UN peacekeeper in Sudan conflict
