Scientific tests on beef products sold in Tesco, Lidl, Aldi, Iceland and Dunnes Stores uncovered low levels of the animal's DNA.
Professor Alan Reilly, chief executive of the Food Safety Authority of Ireland (FSAI), said there was no health risk but also no reasonable explanation for horse meat to be found.
"The products we have identified as containing horse DNA and/or pig DNA do not pose any food safety risk and consumers should not be worried," he said.
According to the research by the FSAI, one sample of burger goods, Tesco Everyday Value Beef Burgers, showed about 29% horse meat relative to beef content.
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.
Silvercrest said it was pulling products from sale and replacing them with new lines.
Offending burgers had been sold in Tesco stores in the UK and Ireland.
The FSAI analysed 27 beef burger products with best before dates from last June to March 2014 with 10 of the 27 products - 37% - testing positive for horse DNA, and 85% testing positive for pig DNA.
The DNA tests found horse in the following products: Tesco Everyday Value Beef Burgers 29.1%; Tesco Beef Quarter Pounders 0.1%; Oakhurst Beef Burgers in Aldi 0.3%; Moordale Quarter Pounders in Lidl 0.1%; Flamehouse Chargrilled Quarter Pounders in Dunnes Stores 0.1%; two varieties of Iceland Quarter Pounders 0.1%.
Even lower levels were recorded in Moordale Beef Burgers in Lidl and St Bernard Beef Burgers in Dunnes Stores.
Some 31 beef meal products such as cottage pie, beef curry pie and lasagne were tested, with 21 found to be positive for pig DNA. All tested negative for horse meat.
Another 19 salami products were tested but showed no signs of horse DNA.
Prof Reilly said of the burgers: "Whilst there is 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, there is no clear explanation at this time for the presence of horse DNA in products emanating from meat plants that do not use horse meat in their production process,"
"In Ireland, it is not in our culture to eat horse meat and therefore, we do not expect to find it in a burger."
The retailers have told food safety chiefs they are removing all implicated products from their shelves.
Prof Reilly said traces of other meats would be unacceptable for people who may not eat certain food on religious grounds.
"Likewise, for some religious groups or people who abstain from eating pig meat, the presence of traces of pig DNA is unacceptable," he said.
The FSAI said consumers can return implicated products to retailers.
The FSAI analysis also found traces of horse DNA in batches of raw ingredients, including some imported from the Netherlands and Spain.
Prof Reilly added: "We are working with the meat processing plants and the Department of Agriculture, Food and the Marine to find out how horse DNA could have found its way into these products."
The FSAI said its officials were working with the Department of Agriculture, Food and the Marine and the processing plants and retailers involved.
Tim Smith, group technical director at Tesco, said: "Today we were informed that the Food Safety Authority of Ireland (FSAI) has found that a number of beef products they have recently tested contained horse DNA.
"These included two frozen beef burger products sold by Tesco in both the UK and Ireland. Products sold at other retailers were also discovered to contain horse DNA.
"We immediately withdrew from sale all products from the supplier in question. We are 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.
"We will not take any products from this site until the conclusion and satisfactory resolution of an investigation.
"The safety and quality of our food is of the highest importance to Tesco. We will not tolerate any compromise in the quality of the food we sell. The presence of illegal meat in our products is extremely serious.
"Our customers have the right to expect that food they buy is produced to the highest standards.
"The relevant authorities have said that these findings pose no risk to public health. We understand that many of our customers will be concerned by this news, and we apologise sincerely for any distress. Our customer service team is standing by to answer any questions customers may have."
Aldi said they were conducting their own investigation.
"We have sought information from one supplier, Silvercrest, which is dealing directly with the FSAI on the issue that has been raised," the company said.
In a statement, Lidl said it has taken the decision to remove all implicated products from sale pending a full investigation.
"A refund will be provided to customers who wish to return affected products," said a spokesman.
The Irish Farmers Association, which is holding its AGM in Dublin, said they were very concerned at the findings.
John Bryan, president of the organisation, demanded the Department of Agriculture urgently investigate the matter.
"Nothing or no-one can be allowed compromise the high standards and reputation of Irish-produced food," he added.