"Elements from the Sudan Liberation Movement refused to comply with police who were trying to arrest them," the minister said.
But Tayeb Khamis, SLM spokesman, told AFP that police had sparked the fighting while trying to get the former rebels to hand over two of their members in connection with "a traffic problem" earlier in the week.
"SLM members tried to convince the police that the problem could be resolved peacefully but, instead, the commander of the police group gave orders to open fire and raid the residence," Khamis said.
He said police killed four men inside the house and four others in a car. He said the ex-rebels then returned fire, killing two police.
The SLM of Minni Minnawi launched a revolt against the central government in Sudan's western Darfur region in 2003, but three years later signed a peace accord with the government.