The US dairy industry has restated its view that the a2 Milk Company (a2MC) is making false claims in its advertising in the United States.
It also added a2MC could be taken to court, though that would be up to the Federal authorities to decide.
The dispute began over a2MC's claim to market a milk product without a protein that it says some people find hard to process.
It pushed this hard in the US, with slogans saying its milk is "easier on digestion" and "may help some avoid discomfort".
This led the US dairy lobby group, the National Milk Producers Federation, to complain that a2MC was making false claims based on an unreliable and clinically insignificant study.
a2 managers in this country shrugged off those complaints, but a senior executive at the National Milk Producers Federation, Clay Detlefsen, has repeated his view that a2MC was using unsound science.
"a2milk company pointed to a number of studies that we view as not being substantial enough to support the claims they have been making," Mr Detlefsen said.
"These studies are too short, they have too small a number of participants... and they lacked (scientific) controls."
Mr Detlefsen added two of the studies were done on Han Chinese, whose digestive system was different from that in Americans.
These concerns led America's dairy lobby, the National Milk Producers Federation, to file a complaint with the self-regulating forum of the US advertising industry, the National Advertising Division.
This in turn referred the matter to the Federal Trade Commission, which has not made any comment so far.
But Clay Detlefsen said the matter was not over yet, and could end up in court.
"The National Advertising Division of the Better Business Bureau extended an offer to the a2 Milk Company to go through the voluntary process of defending their claim.
"The a2 Milk Company chose not to partipate, and therefore the National Advertising Division has referred the matter to the Federal Trade Commission for its review and potential prosecution"
When this matter first arose, a2MC said it was disappointed, but not surprised, at what it called an unfounded challenge, and it planned to continue marketing its product.
In a new statement, the company said there was a large and growing body of work supporting its proposition that a2-only dairy products benefit customers in the way the company said.
It added the Han Chinese study was just one of many, and it was wildly inaccurate to say the studies did not have scientific controls.
There had been official approval in California and support from customers.