“It’s a disappointment to put it mildly given the high level of integrity and credibility we have achieved,” the Taoiseach told reporters.
Read more: BSE: Everything YOU need to know
Mr Kenny said contacts in Irish beef markets abroad had been told of the case and they had been fully briefed on all the precautionary measures which were put in place.
He said that in essence Ireland’s cattle disease status would not now be upgraded to one of being free from monitoring and this meant the previous monitoring regime will continue. But on the other hand Ireland’s disease rating would not be worsened.
“It’s a setback but it puts us back to a situation we were in,” the Taoiseach said.
Mr Kenny added that he expected the Co Louth will be definitely rated as positive.
The suspected case comes just after the World Animal Health Organisation (OIE) moved to recognise Ireland as a country having a "negligible risk" for bovine spongiform encephalopathy (BSE).
Mr Coveney told News At One that this is "a single isolated case".
"It's not confirmed and it won't be confirmed for another week or so. We're satisfied that the likelihood here of BSE is such in this one animal that we need to be fully transparent and officially issue a statement on it.
"We've already made contact with our key trade partners to let them know what happened. The irony of this is that we got the all clear from the international body [OIE] which said Ireland is of 'negligible concern'.
"On one level this is reassuring.. what we have is a very robust system whereby if any animal dies on a farm it gets BSE tested. No animal can die in Ireland on a farm without being tested for BSE.
"There is absolutely no human risk here. This is an animal health issue. Of course it's important because of the reputational issue. It has been the view of most people that the problem of BSE was over for Irish agriculture.
"What we have here is an isolated case of a rare breed of cow in Co Louth that died on the farm that got picked up through our systems. We now have a full investigation to understand how that could have happened.
"We are moving quickly to reassure everybody that this is an isolated case," he told the RTE radio show.
Mr Coveney had recently stated the move to downgrade Ireland’s BSE status was worth in the order of €25m per year to the meat processing sector, as it reduced the list of materials from cattle which have to be disposed of as specified risk materials.
He recently said that BSE had caused “very considerable disruption to trade in the beef sector in the past”.
The department has said that it expects the case to be confirmed as a "classical case of BSE".
This could impact on Ireland’s recently awarded “negligible risk status” from the World Organisation for Animal Health (OIE).
If the case is confirmed, Ireland will revert to “controlled risk status” which applied up to last week and which facilitated trade to a wide range of international markets.
It will also result in the continuation of the existing range of controls for a further number of years.
The case was identified through the Department’s on-going surveillance system on fallen animals (that is animals which die on farms).
Giving his reaction to the news, local TD and former minister Fergus O'Dowd said the test results are "deeply concerning" and have potentially serious implications for the country.
Speaking to Independent.ie, Mr O'Dowd said: "This is very worrying and is deeply concerning for the sector."
He said he was contacted by Minister Coveney this morning and that he was reassured that the results came by way of the department's own surveillance system.
Mr O'Dowd also said that it was important to note that the animal in question had not entered the food chain.
He said he is to get an urgent briefing from the Department of Agriculture this afternoon.
Irish Farmers’ Association (IFA) president Eddie Downey said the discovery of the case shows the “effectiveness of the monitoring and control systems” in place in Ireland.
He said the traceability and monitoring controls adopted by farmers and the sector are the most stringent and robust anywhere and ensure the health status and quality of our agri-produce.
Junior Minister and County Louth TD Ged Nash told Independent.ie that the news of the suspected case of BSE in the county is "disappointing".
He said: “I am due to meet with Department of Agriculture inspectors later today for a full briefing."
Mr Nash stressed there is no risk to human health as a result of this suspected case.
"While it is disappointing that a suspected case of BSE has been identified in County Louth, at this point it seems to be an isolated case. A full investigation is now underway by the Department of Agriculture and I will be keeping a close eye on these developments,” he added.