The local commander of the government troops, known as Rapid Support-2, was reported killed.
"Our forces launched (a) big offensive in Daldako", Arnu Ngutulu Lodi, spokesman for the Sudan People's Liberation Movement-North (SPLM-N), told AFP late Saturday in an email.
Fighting continued into Saturday evening, Lodi said.
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Troops from Rapid Support-2 said they had seized the strategic Daldako area, 17 kilometres (11 miles) northeast of South Kordofan's state capital Kadugli, on May 18.
Two days later they flew journalists to the area, allowing a rare visit to a war zone where access is tightly restricted.
Troops held a victory rally, followed by another one the next day in the capital Khartoum.
But on Sunday the Al-Sudani newspaper, quoting Defence Minister Abdelrahim Mohammed Hussein, said the Daldako field commander of Rapid Support-2 had been killed in the rebel counter-attack.
He said government forces defeated the rebels but Colonel Hussein Jeber al-Dar lost his life.
"He was a brave man," the newspaper quoted Hussein as saying.
Sudan's military spokesman could not be reached for comment but the Facebook page of Rapid Support said Dar had died. It gave no details about the cause of death.
