Retailers hold the "ultimate responsibility" for making sure that horsemeat is not in their products, environment secretary Owen Paterson said today.
After attending an emergency meeting with bosses from leading supermarkets and the Food Standards Agency (FSA) to discuss the scandal, Mr Paterson said retailers would have to start doing their own testing.
"Ultimate responsibility for the integrity of what is sold on their label has to lie with the retailer", Mr Paterson said.
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Mr Paterson said that during this morning's talks the supermarkets agreed to work with the FSA to report their test results on a quarterly basis.
Mr Paterson said investigations would find whether "either gross incompetence or criminal acts" were at fault.
He warned of a possible "international criminal conspiracy" being behind the scandal.
"If there's a criminal act we will work with the authorities wherever they are to ensure the appropriate measures are taken," he added.
"It's a straight fraud. If a product says it's beef and you're actually buying horse, that is a fraud.
"It is in the interests of everyone to get this resolved as rapidly as possible."
Bosses from leading supermarkets including Tesco, Sainsbury's, Asda and Morrisons attended the meeting at the Department for Environment, Food and Rural Affairs (Defra) in London.
The FSA have asked retailers and processors to test all their processed beef products to make sure they are what they say they are, with the results expected by next Friday.
"There may well be more bad results coming through, that's the point of doing this random analysis," Mr Paterson said.
Asked if there were any plans to test for traces of other meats, such as dog, the environment minister 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products on sale in British supermarkets this morning, but I would not recommend anyone to eat a product which has been withdrawn."
The talks come as frozen food company Findus UK reiterated its apology after tests found up to 100% horse meat in some of its beef lasagnes.
Supermarket chain Aldi confirmed that two of its ready meal ranges produced by Comigel, the French supplier also used by Findus, were found to contain between 30% and 100% horse meat.
And last night, the issue became a police matter as Scotland Yard announced they had met representatives from the FSA.
Mr Paterson added: "This is a conspiracy against the public. Selling a product as beef, and including a lot of horse in it is fraud."
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.
He said the supermarkets had agreed to look into how they can improve their existing regimes and have already begun plans to carry out more testing.
They had also agreed that consumers should be compensated if they have bought withdrawn products, with no questions asked.
Prime Minister David Cameron has said the matter is "shocking" and "completely unacceptable".
Labour leader Ed Miliband described the situation as "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".
Scotland Yard said officers had met the FSA over the scandal, although there is currently no official police investigation.
Politicians and food safety experts have played down the risk to human health, with Mr Cameron, speaking in Brussels, saying it was not about food safety but accurate food labelling and the industry would have to work hard to restore confidence.
Findus UK confirmed 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 Findus spokesman added that the firm "do not believe this is a food safety issue" but that anyone who had bought 320g, 360g or 500g Findus beef lasagne packs could call its customer care line on 0800 132584 for advice and a refund.
The frozen food 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, the FSA said.
Labour MP Tom Watson published a letter on his website which he claimed was sent by Findus to retailers on Monday, warning that a France-based supplier had told it there may be problems with raw materials delivered since August 1 last year.
In it, the firm claimed raw materials delivered to a French contractor since August 1 were "likely to be non-conform and consequently the labelling on finished products is incorrect".
The letter added: "The supplier has asked us to withdraw the raw material batches."
But Findus said it was not aware of any contamination with horse meat last year.
The company said in a statement: "Findus want to be absolutely explicit that they were not aware of any issue of contamination with horse meat last year.
"They were only made aware of a possible August 2012 date through a letter dated 2 February 2013 from the supplier Comigel. By then Findus was already conducting a full supply chain traceability review and had pro-actively initiated DNA testing."
The statement added that Findus had not been invited to the Defra summit although the Food and Drink Federation, of which they are a member, was attending.
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 horsemeat, the Department for Education said schools and councils were responsible for their food contracts.
A spokeswoman for the Local Authority Caterers Association (Laca) 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.
Findus later confirmed it was taking legal advice.
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.
"The early results from Findus UK's internal investigation strongly suggests that the horsemeat contamination in Beef Lasagne was not accidental."
Meanwhile, work is under way to ensure Scottish-based manufacturers of processed meat products have the necessary measures in place to prevent contamination following the horsemeat scandal.
Public Health Minister Michael Matheson said the FSA in Scotland has made arrangements for local authorities to carry out a series of food standards inspections on top of "stringent" controls already in place.
The minister said: "The initial focus will be on manufacturers of processed meat products and this work is already under way.
"It is the responsibility of the food industry to produce safe food that is accurately labelled and does not mislead consumers.
"Scotland already has a stringent set of regulatory controls in place to underpin food safety and confidence but we are determined not to be seen as in any way complacent.
"That's why we are speaking with the FSA on a daily basis to ensure we are fully engaged with this situation as it evolves."
Rural Affairs and Environment Secretary Richard Lochhead said action was "essential" to prevent any damage to the reputation of Scotland's food industry.
Mr Lochhead said: "It is completely unacceptable that consumers are being misled about what is contained in the food that they buy, and that multi-national companies have allowed this to happen.
"While no manufacturers based in Scotland are currently affected, this is an extremely serious issue which, understandably, is creating a great deal of alarm amongst consumers.
"I am urging the European Commission and the UK Government, who have responsibility in this area, to get to the route of this matter immediately.
"While no food safety risks have been identified by the FSA so far, it is essential that this scandal is addressed to eliminate the public's sense of confusion and to prevent any damage to Scotland's highly regarded food industry whose success is built on a reputation for quality."