Investigations are under way to try to find out how beef burgers on sale in UK and Irish Republic supermarkets became contaminated with horsemeat.
Irish food safety officials, who carried out tests two months ago, said the products had been stocked by a number of chains, including Tesco and Iceland stores in the UK.
They said there was no human health risk and the burgers had been removed.
Tesco said it was "working... to ensure it does not happen again".
The Food Safety Authority of Ireland (FSAI) said the meat had come from two processing plants in the Irish Republic - Liffey Meats and Silvercrest Foods - and the Dalepak Hambleton plant in Yorkshire.
The burgers had been on sale in Tesco and Iceland in the UK and the Republic of Ireland, where they were also on sale in Dunnes Stores, Lidl and Aldi.
A total of 27 burger products were analysed, with 10 of them containing traces of horse DNA and 23 containing pig DNA.
Horsemeat accounted for approximately 29% of the meat content in one sample from Tesco, which had two frozen beef burger products sold in both the UK and Ireland contaminated with horse DNA.
In addition, 31 beef meal products, including cottage pie, beef curry pie and lasagne, were analysed, of which 21 tested positive for pig DNA.
The director of consumer protection at the FSAI, Raymond Ellard, said several investigations would now need to take place.
He said: "The companies have taken a very responsible attitude. On a voluntary basis they have withdrawn products from sale, so have the retailers.
"They are co-operating completely with the authorities here to investigate how this could have happened. A long chain of enquiry has to take place now to look at all the raw ingredients that we use for these productions, where they came from and how the cross contamination could have occurred."
Tesco's group technical director, Tim Smith, stressed the company "immediately withdrew from sale all products from the supplier in question" after receiving the test results on Tuesday.
In a statement, Mr Smith said food safety and quality was "of the highest importance to Tesco" and "the presence of illegal meat in our products is extremely serious".
He added Tesco was "working with the authorities in Ireland and the UK, and with the supplier concerned, to urgently understand how this has happened and how to ensure it does not happen again".
FSAI chief executive, Professor Alan Reilly, said there was "a plausible explanation for the presence of pig DNA in these products, due to the fact that meat from different animals is processed in the same meat plants".
But he added: "There is no clear explanation at this time for the presence of horse DNA in products emanating from meat plants that do not use horsemeat in their production process.
"In Ireland, it is not in our culture to eat horsemeat and, therefore, we do not expect to find it in a burger.
"Likewise, for some religious groups, or people who abstain from eating pig meat, the presence of traces of pig DNA is unacceptable."
The Irish Minister for Agriculture, Simon Coveney reassured the public that the burgers posed no health risk, adding the Republic of Ireland "probably has the best traceability and food safety in the world".
Iceland said the FSAI's findings were concerning, stressing the company had "withdrawn from sale the two Iceland brand quarter pounder burger lines implicated in the study".
It said it "would be working closely with its suppliers to investigate this issue and to ensure that all Iceland brand products meet the high standards of quality and integrity that we specify and which our customers are entitled to expect".
Aldi said only one of its products - the Oakhurst Beef Burgers (8 pack), which is on sale only in the Republic of Ireland - had been affected.
In a statement, Aldi Stores (Ireland) said it had "immediately removed the product from sale and have launched an investigation into the matter".
The company said it "takes the quality of all its products extremely seriously and demands the highest standards from its suppliers".
Lidl was not available for comment when contacted by the BBC.
Meanwhile, Silvercrest Foods and Dalepak both said they had never bought or traded in horse product and have launched an investigation into two continental European third party suppliers.