The report in the newspaper China Daily follows months of delays in which lawyers for plaintiffs told AFP they were warned not to sue over the scandal, which embarrassed China by exposing chronic holes in food-safety mechanisms.
A senior judicial official said courts were now accepting cases from families who had rejected compensation offers from milk companies involved in the scandal, the newspaper said.
"A small number of the infant victims' parents have not accepted the government-led compensation and have prepared pleas," it quoted Shen Deyong, executive vice-president of the Supreme People's Court, as saying.
"The people's courts (at various levels) have prepared for the work. They will accept the compensation cases according to the law."
At least six infants died and nearly 300,000 were sickened last year by milk powder contaminated by the industrial chemical melamine, which was added to milk supplies to give the appearance of a higher protein content.
A court in eastern China's Shandong province has accepted legal documents from 54 families whose infants developed urinary illnesses from baby milk powder made by Syrutra International Inc., a lawyer told AFP.
"Before this, the court would accept no materials that we sent to them. The court would not reply to us or accept the lawsuit," a Beijing-based lawyer in the case, Li Jinglin, told AFP.
However, he said there was no guarantee the court in the coastal city of Qingdao would take the case.
The company is a Sino-US joint venture, China Daily said.
China Daily also said a court in the northern city of Shijiazhuang had recently contacted lawyers representing 117 families in the city to discuss their cases.
The families want to sue Sanlu -- one of China's biggest dairy producers and the company at the centre of the scandal -- which is based in Shijiazhuang.
The scandal caused kidney stones in thousands of infants who were fed tainted baby milk powder, with those who died succumbing to kidney failure.
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