The Food Safety Authority of Ireland (FSAI), who carried out tests two months ago, tested 27 products and found 10 of them containing horse DNA and 23 pig DNA. The products had been stocked by a number of chains, including Tesco and Iceland stores in the UK, while in Ireland the products were sold in Tesco, Lidl, Aldi, Iceland and Dunnes Stores.
Horse meat accounted for 29.1% of the meat content in a sample of the Tesco Everyday Value Beef Burgers. There was also equine DNA found in Tesco Beef Quarter Pounders.
The beef burger products which tested positive for horse DNA were produced by Liffey Meats and Silvercrest Foods in Ireland and one UK plant, Dalepak Hambleton.
An additional 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.
"The companies have taken a very responsible attitude. On a voluntary basis they have withdrawn products from sale, so have the retailers," he said.
"They are co-operating completely with the authorities here to investigate how this could have happened. A long chain of inquiry 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, said the company "immediately withdrew from sale all products from the supplier in question" after receiving the test results on Tuesday.
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".
The Irish Minister for Agriculture Simon Coveney said: "There is no food safety risk" while FSAI chief executive Prof 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."
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.