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, said Lodi, who could not be contacted on Sunday.
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 the minister 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.
- 'Serious shelling' -
Residents of Kadugli reported hearing heavy outgoing government artillery fire on Saturday morning.
"It was really serious shelling all morning yesterday," one resident told AFP on Sunday. "It was unusual."
Ethnic minority rebels in South Kordofan have been fighting government forces for three years in a largely-hidden war which the United Nations says has affected more than one million people.
Sudan's National Intelligence and Security Service (NISS), which has authority over Rapid Support, invited journalists to Daldako following accusations that a sister Rapid Support unit in Sudan's western region of Darfur had abused civilians.
In an April report, UN chief Ban Ki-moon said Rapid Support elements had attacked and burned villages in Darfur.
After Sudanese opposition leader Sadiq al-Mahdi reportedly made similar comments, NISS agents arrested him on May 17.
Observers have said Mahdi's arrest undermined a dialogue between the ruling National Congress and other political parties aimed at ending Sudan's multiple wars, economic crisis and political divisions.
Mahdi's arrest was a power play by elements of the security service, said Magdi El Gizouli, a fellow at the Rift Valley Institute.
"In presenting itself as a fighting force capable of challenging insurgencies, the NISS is obviously boosting its stature with the ambition to achieve the kind of political recognition that the SAF continues to enjoy," Gizouli said last week.
The Sudanese Armed Forces (SAF) are distinct from the military units of NISS.
An AFP reporter who visited Daldako on Tuesday found Rapid Support troops digging trench defences.
More than 1,000 men were spread across a three-kilometre zone in Daldako with tanks, artillery, anti-aircraft guns and recoilless rifles.
Dar, with a slight moustache and carrying an officer's wooden staff, met reporters there.
Wearing a green beret pulled down at a slight angle, he had a NISS patch above the rolled-up sleeves of his light-brown uniform.
"This is a strategic area for the rebels and it was the main threat to Kadugli's security," Dar said.