"Thirty-two people were killed and 20 others wounded ... One of UNISFA [UN Interim Security Force for Abyei] peacekeepers was killed," Kuoch was quoted as saying by Eye Radio.
The minister added that UNISFA peacekeepers intervened in the clashes and managed to stop them.
The oil-rich Abyei region has been a disputed territory between Sudan and South Sudan since the latter gained independence in 2011. That same year, the UN Security Council established the UNISFA to monitor tensions along the border, facilitate the delivery of humanitarian aid and use force to protect civilians and aid workers.