In the United States, inspections have been stepped up at ports on shipments of bulk food ingredients from Asia that are derived from milk.
The US Food and Drug Administration warned consumers on Saturday not to buy milk products from China over the internet.
Chinese authorities say melamine was put into the milk powder to make it appear the product had more protein.
The chemical, normally used to make plastics and glues, is rich in nitrogen, an element often used to measure protein levels, and so can be used to disguise diluted milk.
It is being blamed for causing kidney stones in the affected babies, a condition that is rare in infants but which causes a range of health risks.
Grocery stores across China continued to remove milk and other dairy products from shelves on Saturday.
In Beijing and Shanghai, the dairy sections of many stores were empty, a day after health officials said the scare, which had initially affected only baby formula, had spread to liquid milk, ice-cream and yoghurt.
A senior dairy analyst told the AP news agency that Chinese farmers were cutting corners to cope with the rising costs of feed and labour.
Chen Lianfang, an agribusiness consultant, said: "Before the melamine incident, I know they could have been adding organic stuff, say animal urine or skin - basically, anything that can boost the protein reading."
But he and others expressed scepticism that so many farmers would know to add melamine to milk.
"The chemical is not water-soluble and must be mixed with formaldehyde or another chemical before it can be dissolved in milk.
"Farmers can't be well-educated enough to think of melamine ... There must be people from chemical companies contacting them and telling them it's a good idea," Chen said.
The Chinese government has said it will introduce a new food-monitoring system in response to the crisis - the latest in a series of safety scandals to rock China's food and manufacturing industries.
The government's General Administration of Quality Supervision, Inspection and Quarantine (AQSIQ) said tests showed nearly 10 per cent of samples taken from Mengniu Dairy Group and Yili Industrial Group - China's two largest dairy companies - contained melamine.
A third firm, the Shanghai-based Bright Dairy, has also been found to have sold contaminated products.
In Hong Kong, the authorities ordered a recall after China-made dairy products sold there were found to contain the toxin.
Al Jazeera's Laura Kyle, reporting from Beijing, said the scale of the scandal and fallout could be far wider than initially thought, with possibly tens of thousands of people affected.
Coffee chain Starbucks has already pulled milk supplied by Mengniu from its more than 300 cafes in mainland China.