The rebel Sudan People’s Liberation Movement-North (SPLM-N) said the workers are safe and “in good health”.
China’s foreign ministry confirmed that some of their nationals were missing, but did not specify how many.
South Kordofan is one of three areas hit by conflict since South Sudan became independent from Sudan in July.
Abyei and Blue Nile along with South Kordofan lie along the loosely demarcated border between Sudan and South Sudan.
The Chinese nationals are reported to have been working on road construction projects in the area.
“Yes, we have captured them,” Arnu Ngutulu Lodi of the SPLM-N told the AFP news agency. “I want to assure you right now they are in safe hands.”
Arnu Ngutulu Lodi said they were captured – along with nine Sudanese soldiers – after the SPLM-N attacked and destroyed a Sudanese military convoy in the area.
Sudan’s army said the rebels had attacked the compound of a Chinese construction company and captured 70 civilians.
“Most of them are Chinese. They are targeting civilians,” army spokesman Sawarmi Khalid Saad told Reuters news agency.
He said the army had launched an operation to rescue them.
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