Published Thursday, 21 August 2014
Edwin Poots had asked for £160m in the latest budget review, but only received £20m.
He told UTV that this was not enough and if cuts have to be imposed, the Executive will have to put them into effect because he will refuse.
The DUP politician also said that he will not resign from his ministerial position.
Mr Poots said: "Where I have a problem is that this is going to impact upon services such as oncology and cancer services, cardiac services, support for organisations like Hospice, support for voluntary organisations who are carrying out essential services for families, emergency departments, out of hours doctors.
"All of these things will be impacted and impacted negatively and will have profound and devastating consequences for the Northern Ireland public," he said.
"It is not doable to deliver the quality of health service that the Northern Ireland public require with the budget that has been offered. We really need to look at this again."
He continued: "I will work very hard to make savings that won't have that negative impact on the public, but I am not prepared to make cuts that will have those devastating consequences.
"Do they find another Minister who is prepared to do it, do they find the money that enables me to do it, or do the Executive make these decisions at an Executive level to make those cuts?"
Sinn Féin accept there is a problem with funding.
However, the party said that it is an argument Stormont ministers shouldn't be having with them - but with the British government.
Alex Maskey, SF's South Belfast MLA, said: "All of the parties had a say in where the budget would be landed on each of the departments.
"So all of the departments - including the health department - had their say in those discussions and, in fact, negotiations around June and therefore, it's up to all the parties, the ministers and their departments to fight their case."
He continued: "There's no question that there are budget problems across all of the departments - every single department here has been affected by the cuts which are imposed by London.
"And the problem for me is that the DUP and Edwin Poots need to take their battle to Westminster.
"The British government are the people who are cutting the budget here not Sinn Féin.
"We opposed the welfare cuts that the Tories - and the DUP - wanted to impose in June."
However, with Stormont is still in recess, welfare reform still unresolved and remains on the agenda for the Assembly's return next month.
© UTV News