As senior officials invited Polish vets to examine the meat and relevant documentation, Simon Coveney confirmed Garda officers were heavily involved in a major investigation.
Northern Ireland's deputy First Minister Martin McGuinness has also called for a Police Ser-vice of Northern Ireland inquiry as the affair threatens confidence in Ireland's meat industry.
Irish Taoiseach Enda Kenny has committed to resolving the problem after food safety chiefs warned of "fraudsters" drip feeding contaminated products into the food chain.
Rangeland Foods in Co Monaghan was one of the latest plants shut down after a sample at the factory tested positive with a reading of 75% horse DNA in raw ingredients, authorities said.
The company supplies burgers to one of Ireland's most popular fast-food chains, Supermac's, but the restaurant's chief executive, Pat McDonagh, has insisted he is sure all his burgers are 100% Irish.
The highest level of equine genetic material has been found in a quantity of frozen meat being stored in Northern Ireland.
Freeza Meats in Newry had meat which was 80% horse, which the UK's Food Standards Agency said was potentially linked to the Silvercrest factory in the Republic of Ireland, one of the first processors to be named in the scandal.