BEIJING >> Workers on strike at a Chinese factory owned by the world’s largest maker of athletic shoes have rejected management’s latest offer in an ongoing labor dispute that is crimping production for brands such as Nike and Adidas.

The on-off work stoppage at Yue Yuen Industrial (Holdings) Ltd.’s massive factory complex in southern China, which employs more than 40,000 workers, has stretched into the second week as both sides have failed to reach an agreement.

The dispute erupted over underpayments for social security and housing fund payments required by Chinese law. It has become one of the largest strikes in China’s private sector, where low-cost manufacturers are facing increasing labor activism amid a shortage of migrant workers that is pushing up labor costs.

Tens of thousands of workers remained off the job Tuesday, according to workers and labor groups, after they rejected the company’s latest offer, which included making up back payments for social security and housing, full contributions for those benefits starting May 1 and a $37 monthly cost of living allowance.

“We’ll pay what is in the regulations, there should not be any concern on that,” Yue Yuen spokesman George Liu said.

The workers at the Dongguan plant are demanding a 30 percent pay raise and a better-worded commitment to future contributions. They also say it’s unfair that workers would be required to make up their share of missed contributions from the past. And they want their own representatives to negotiate with management.

Greg Rossiter, of Nike Corporate Communications in Beaverton, Oregon, said in an email that Nike was “aware and concerned by the events at the Yue Yuen factory” and was monitoring the talks between the management and workers.

Another, smaller Yue Yuen plant in Jiangxi province was hit by a brief strike on Monday that also centered on social security payments but for the opposite reason. Liu said workers slowed production because they didn’t want to make full payments, which would leave them with less take-home pay. The dispute ended after the plant, which employs 6,000, enlisted local government officials to tell the workers the payments are required by law.

The two sides in the Dongguan strike appeared far from agreement.

“We are not quite sure who to come to a deal with,” Liu said, adding that the dispute was having an impact on production and the company has made contingency plans to shift work to its other factories in Vietnam and Indonesia.

Yue Yuen workers at the Dongguan plant waited in their dorms. “We just rest at home and get some sleep,” said 31-year-old Cui Tiangang, who cuts and glues rubber soles at a Yue Yuen factory. “Some play cards and so on. Kind of boring now.”

He said workers are worried about losing their jobs but are unwilling to accept the Yue Yuen offer.

“As far as I know, none of the workers around me would like to accept the offer,” Cui said. “Some have worked there for more than 10 years, and in this case, they need to pay like 20,000 to 30,000 yuan (to make up the missed social security payments). It is too hard for the workers.”

Li Qiang of New York-based China Labor Watch said calculations by Yue Yuen workers show the $37 monthly allowance is not enough to make up for the full contributions required for the social security and housing programs.

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Chan reported from Hong Kong, and Associated Press researcher Fu Ting in Shanghai contributed to this report.