Environment Secretary Owen Paterson said the next set of results on all retailers' and manufacturers' processed beef products could reveal further traces of horse meat.
"There may well be more bad results coming through, that's the point of doing this random analysis," Mr Paterson said.
The results, ordered by the Food Standards Agency, are due on Friday,
Mr Paterson said retailers have agreed plans to improved their food testing, adding that they hold the "ultimate responsibility" for making sure their products do not contain horse meat.
One of the food companies at the centre of the horse meat scandal has said it is considering taking legal action against its suppliers.
Frozen foods firm Findus, which has taken its beef lasagnes off shelves after some were found to have up to 100% horse meat in them, said it was looking into legal action as an internal investigation "strongly suggests" that the contamination "was not accidental".
The company said in a statement: "Findus is taking legal advice about the grounds for pursuing a case against its suppliers, regarding what they believe is their suppliers' failure to meet contractual obligations about product integrity."
Mr Paterson spoke after attending an emergency meeting with bosses from leading supermarkets, trade bodies and the Food Standards Agency (FSA) to discuss the scandal which has seen chains including Tesco, Lidl, Aldi and Iceland withdraw some products.
He said supermarkets and trade bodies have already begun plans to carry out more testing and report their results on a quarterly basis.
He said it was down to retailers to visit manufacturers and make sure they stick to the proper protocols to be sure themselves that the materials going into their products are what they are meant to be.
They had also agreed that consumers should be compensated if they have bought withdrawn products with no questions asked, he said.
Mr Paterson added: "It's a question of either gross incompetence, but as I've said publicly and I'll repeat again, I'm more concerned there's actually an international criminal conspiracy here, and we've really got to get to the bottom of it.
"If there's a criminal act we will work with the authorities wherever they are to ensure the appropriate measures are taken.
"This is a conspiracy against the public. Selling a product as beef, and including a lot of horse in it is fraud."
Bosses from supermarkets including Tesco, Sainsbury's, Asda and Morrisons attended the meeting at the Department for Environment, Food and Rural Affairs in London after the issue became a police matter.
Scotland Yard have met representatives from the FSA, although there is currently no official police investigation.
Asked if there were any plans to test for traces of other meats, such as dog, the Environment Secretary said: "It may be very isolated, it might be a small number of suppliers involved in the horse trade we don't know, but I think that as we progress and we'll know more over the course of the next few weeks, we can decide what to do next."
Questioned about whether he would be prepared to eat meat bought from a supermarket, he said: "I would be very happy to eat any products on sale in British supermarkets this morning, but I would not recommend anyone to eat a product which has been withdrawn."
Prime Minister David Cameron described the matter as "shocking" and "completely unacceptable", while Labour leader Ed Miliband said it was "appalling".
He added: "I think people in the country will be quite shocked that horse meat has been in the food that they have been innocently buying.
"The Government has got to get a grip on this situation."
The Trading Standards Institute has said the discovery of such high levels of horse meat suggests "deliberate fraudulent activity".
Food safety experts have said there is no risk to public health.
Findus said it carried out a full product recall on Monday, two days before DNA tests found that some of its lasagnes contained up to 100% horse meat.
The firm, which has its headquarters in London, tested 18 of its beef lasagne products, made by French food supplier Comigel, and found that 11 contained in the range of 60% to 100% horse meat.
Tesco and Aldi have also withdrawn a range of ready meals produced by Comigel over fears that they contained contaminated meat.
The GMB union said all hospitals, schools and meals-on-wheels services should verify that horse meat had not been served to vulnerable people.
Responding to fears that school dinners might be contaminated with horse meat, the Department for Education said schools and councils were responsible for their food contracts.
A spokeswoman for the Local Authority Caterers Association said: "We are as sure as we can be that this is not affecting the school catering area."
She added that there were "strict guidelines" around food safety and supplying dinners in schools, including transparency and traceability of ingredient provenance, written into contracts.