The interior ministry said the attack was on a base for central reserve forces, a branch of the police.
The fighting came just days before Ban Ki-moon, the UN secretary-general, was due to arrive in Sudan to try to set a timetable to revive Darfur peace talks between the government and rebels after a May 2006 deal faltered.
The rebels said the base they attacked was the logistical and supply centre for ongoing attacks in South Darfur, where rebels say an aerial bombing campaign has driven thousands of people from their homes over the past month.
Ban, due to arrive on Monday, has deplored the recent surge of violence as "simply unacceptable" and has condemned the government bombardment as a violation of a UN Security Council resolution.
The Sudanese interior ministry statement said that following the Kordofan attack, a combined force of police and armed forces pursued the rebels and captured a number of them in an ambush. It did not say how many rebels it captured.
"They will face justice and these measures will apply to all those who supported this criminal act," the ministry said.
International experts estimate 200,000 people have died since mostly non-Arab rebels took up arms in early 2003 accusing the central government of neglecting the region. The Sudanese government denies the charge and says 9,000 have died in Darfur.