Members could include a lay person representing consumers, and specialists such as scientists - possibly even a Chinese scientist.
Prime Minister John Key said last night it was important that the powers of those undertaking the inquiry were "absolutely spelled out" and that all eventualities were catered for.
"We need to make sure that the inquiry has broad-ranging powers."
Mr Key said he was keeping his distance from Fonterra at present. He had had some informal text message exchanges with chief executive Theo Spierings.
"I had an invitation to have a longer conversation with them on Friday. I deliberately chose not to at this point," he told the Herald.
"This is a serious matter and needs to be treated professionally.
"It's not that I am not prepared to sit down with the management - I am. But it needs to be done formally."
Asked what he thought about Mr Spierings' comment "human errors in life do happen", Mr Key said the role of the company and the regulator was to eliminate or rectify any human error before it became a problem.
"That's the issue at heart here. Did the company do enough testing? Was it reasonable to expect them to have conducted more tests and should this ingredient have been stopped from further processing prior to the point where the Government was advised there was a potential problem?"
Fonterra's woes continued yesterday as Sri Lanka recalled two batches of milk powder which it claimed were contaminated with the farm chemical DCD.
Mr Spierings said the company would fight the claim, while the Government said the Sri Lankan tests were flawed.
"We have been asked by the Ministry of Health to recall two batches of product tested by ITI [Sri Lanka's Industrial Technology Institute] last month," said Leon Clement, managing director Fonterra Brands Sri Lanka.
The recalled products, which had been removed from shops, did not contain any DCD, he said.
"As widely reported, Sri Lanka does not have the required technology to test for DCD in milk products," Mr Clement said.
"The ITI test results have been analysed by an independent and internationally recognised expert in analytical chemistry, Professor Brynn Hibbert, who has found that they are not accurate."
Mr Key described Fonterra as "the poster child" for New Zealand exporting on TV One yesterday.
He also said at the weekend he would go to China after an inquiry when he had answers to give about what had happened and what had been done in the aftermath.
- Additional reporting Teuila Fuatai of APNZ