Taoiseach Enda Kenny has insisted that hospitals have been given increases of 3% in budgets this year and that the coalition is cutting costs and not services.
His comments come after a letter to the HSE from CEOs of four of the country's biggest hospitals warning that cuts were leading to safety risks in the delivery of services.
The letter was written by the chief executives of Tallaght Hospital, St James's Hospital, the Mater and Our Lady's Hospital for Sick Children.
In the Dáil, Enda Kenny rejected a call from Sinn Féin for the resignation of Health Minister James Reilly.
Mr Kenny said the Government is not ignoring the letter from the chief executives in the four hospitals.
"It's an important letter, and it's not being treated as a joke, believe you me," he said.
"It's a serious business, but it's also a serious business… to change the structure of the way that health services are delivered for people; to cut the costs of deliving those services but not the services themselves.
"And I do hope that constructive engagement takes place with these chief executives."
However Stephen McMahon of the Patients Association said the fact that the CEOs of the hospitals wrote to the HSE highlights just how serious the problem is.
"The fact of the matter is that patient safety is paramount in our healthcare system; and if individuals are finding it frustrating that they don't believe that their concerns are not going to be listened to, out of frustration people go to all sorts of avenues to have their voice heard," Mr McMahon said.
"The key thing here is this unprecedented move by the CEOs have put up a red flag."