BEIJING, China (CNN) -- The number of children sickened by suspected melamine-tainted milk products in China has more than doubled and apparently spread beyond mainland China -- raising fears that the impact of the tainted products could be more widespread that initially thought.

China's Health Ministry announced Sunday that 12,892 infants and young children have been sickened by tainted milk powder -- more than double the number previously reported -- according to state-run Xinhua news agency. Of these, 104 have serious symptoms, and 1,579 have been cured and discharged, the agency said.

Previously, Chinese officials said more than 6,200 children had been sickened by melamine found in baby formula. At least four children have died. Xinhua reported the first death from from the toxin on September 12.

In addition, nearly 40,000 other infants and young children have received outpatient medical treatment and consultation as a result of the tainted milk, Xinhua reported on Sunday. Watch CNN visit the company at the center of the scandal »

The latest statistics from mainland China come after Hong Kong reported late Saturday that a 3-year-old girl has been sickened by a suspected melamine-tainted milk product -- the first known illness outside of mainland China.

The child in Hong Kong was diagnosed with a kidney stone at Princess Margaret Hospital, the government reported, citing a hospital statement. Although tests are still ongoing, her illness is suspected to be linked to consuming milk products containing melamine, the hospital statement said.

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The child has been released, and her condition will be monitored, it said.

Meanwhile, Hong Kong's Center for Food Safety announced Sunday that a sample of Nestle Dairy Farm Pure Milk, sold in one-liter packs for catering use only, had tested positive for melamine. But the Swiss company said in a news release it is "confident" none of its milk products made in China contains the chemical.

The officials asked that retail sales of the milk for catering be halted, and that Nestle recall the product.

"The level of melamine detected in the Nestle sample was 1.4 ppm (parts per million), which the center believed is low. However, small children should not consume the product," the center said. Learn more about the chemical melamine »

The other 64 samples were free from the toxic substance, according to the Hong Kong government Web site.

In a news release on its Web site, Nestle did not address the report regarding its Dairy Farm Pure Milk, but it disputed press reports that -- according to Nestle -- said melamine was found in its powdered toddler milk formula, NESLAC Gold 1+, designed for children ages 1 to 3.

"Following press reports in Hong Kong earlier today claiming that traces of melamine had been found in a Nestle growing up milk, Nestle is confident that none of its products in China is made from milk adulterated with melamine," the company said.

"The Hong Kong Government's Food and Environmental Health Department has just released a report declaring that NESLAC Gold 1+, which was mentioned in the media reports, is safe and that no melamine was detected in the product," Nestle said.

The company, based in Vevey, Switzerland, said NESLAC Gold 1+ also was tested by at least two government-approved, independent laboratories, and none of them detected melamine in the mixture.

"Over 70 different tests are routinely conducted in the course of producing infant formula and other milk products," Nestle said. "In fact, the Chinese authorities have issued official certificates for all tested Nestle products stating that no melamine has been detected in any of them."

Nestle noted that "melamine is found throughout the food chain across the world in minute traces which do not represent any health risk for consumers." It noted that a 3-year-old would have to consume over 40 liters of milk that contained 2 ppm of melamine to exceed internationally recognized safety limits, which vary by country.

Melamine is commonly used in coatings and laminates, wood adhesives, fabric coatings, ceiling tiles and flame retardants. It has shown up in testing done on milk and yogurt, prompting at least two supermarket chains in Hong Kong to pull dairy products by Mengniu and Yili from store shelves, representatives from the companies told CNN Friday.

Health experts say ingesting melamine can lead to kidney stones, urinary tract ulcers, and eye and skin irritation.

The Chinese State Administration of Quality Supervision, Inspection and Quarantine said the amount of the chemical found in the milk would not cause ill effects in adults who drank less than two liters a day.

More than 18 people have been arrested in the contaminant cases.

Melamine is the same industrial contaminant from China that poisoned and killed thousands of U.S. dogs and cats last year. The chemical, a byproduct of plastic manufacturing, can be used to mimic high-protein additives.

All About China • Food Safety • Product Recalls • Hong Kong