"Deliberate contamination of foods intended for consumption by vulnerable infants and young children is particularly deplorable," the WHO and Unicef said in Thursday's statement.
They added, however, that they expected "swift and firm" government action and plans to overhaul food monitoring and inspection processes would prevent a recurrence.
|Scores of milk products have been recalled from shop shelves [Reuters]
"We also expect that following the investigation and in the context of the Chinese government's increasing attention to food safety, better regulation of foods for infants and young children will be enforced," the statement said.
However, the agencies also said the scare underscored the advice of health professionals who have urged mothers to, where possible, breast feed their infants.
Many Chinese parents said they were persuaded to use infant formula by advertising which said the formula was more nutritious than breast milk.
On Thursday, Vietnam, Nepal and South Korea became the latest to join a growing list of countries banning the import of Chinese-made products containing powdered milk.
"Korea Food and Drug Administration will prohibit importing of Chinese food products which include materials like powdered milk, until the safety of Chinese food products is ensured," South Korea's food safety chief Choi Sung-rak told reporters.
In Taiwan, a list of more than 160 products containing Chinese milk and vegetable proteins is being recalled to be destroyed after the tainted milk was found to have affected an array of foods, including cereals, sweets and biscuits.
|About 54,000 children have been affected by the contaminated milk [Reuters]
The scare initially centred on baby formula made by China's Sanlu dairy group, but investigations have since found the contamination has extended into many other companies and products.
In China the government has begun to help the struggling dairy industry as confidence in it has been hit hard by the scandal.
In some supermarkets, labels reading "No Melamine Detected" have been placed on inspected products in an attempt to reassure the public about safer brands of milk.
Several Chinese provincial governments are now also promising to subsidise dairy farmers who are facing bankruptcy as demand for milk plummets.
Those in Hebei, the worst-hit province, will receive $29 for each cow they own in an effort to keep them in business.