It comes after the Belfast Health Trust said that families of patients who died after delays in treatment were not fully informed of all the circumstances surrounding their deaths.
Mr Robinson stated on Wednesday evening that if more money is needed to fix the problems at the Royal Victoria Hospital in Belfast - the Health Minister will get it.
"I very much support Edwin," the DUP leader told UTV.
"I make this very clear if Edwin comes to the Executive on the basis of advice from professionals within his department and indicates that the issue is about finance then my hand will come up to give him whatever support he requires because lives must not be put at risk."
This week it has emerged that five people died at the Royal Victoria Hospital partly because they were not treated quickly enough.
I recognise the very difficult task that Edwin Poots has to do and I also see his absolute determination to get to the bottom of these.
Dr Tony Stevens, medical director with the Belfast Trust, told UTV the delay in treatment contributed to the death of the patients last year.
He said: "These five cases were serious adverse incidents, one factor, and one factor alone may have been that the patients waited longer than they should have done."
Health Minister Edwin Poots faced questions at Stormont on Tuesday afternoon about last month's major emergency at the Royal's A&E ward.
The DUP minister, who said he had only just learned about the five deaths in the radio interview, fended off claims from the SDLP of a possible cover up.
He said that, while he had only learned of the deaths, those people that died had been seriously ill and he had asked his officials to look into the matter.
On Wednesday, the Belfast Trust said not all the families had been informed about the delay contributing to the deaths of their loved ones.
A spokeswoman said some of those affected had not wanted all the details.
She said: "Not all of the families have been informed.
"Some of them have said that they do not wish for any further information, however for those that do, we are going back to ensure that they are fully informed."
The latest revelation comes after a report, commissioned by the heath minister, found serious failings in the hospital.
Last month, officials at the hospital were forced to declare a major emergency at the Royal because of the strain on its resources.
Patients faced over 12 hour waits for treatment and extra staff had to be drafted in with some comparing the incident to those of a war zone.
The next day, hospital workers were so angry that they staged a protest and booed the health minister as he was driven away from the facility.
A report by the health watchdog, the Regulation Quality and Improvement Authority, into the incident found that staff were faced with "intolerable pressure", some said they were bullied and the care system was not functioning as it should do.
On Wednesday, the Health Minister Edwin Poots appeared in front of the health committee to answer questions over the latest crisis in the hospital.
During an at times heated health committee hearing at Stormont, it was confirmed the coroner has been informed about four of the five deaths and that two of the families have not been made aware of the circumstances.
The health minister insisted the situation at the Royal is under control.
The former chairman of the Northern Trust believes he was sacked in 2012 after highlighting the problems in Accident and Emergency department at the Antrim Hospital.
Jim Stewart told UTV: "This is the first time I have heard of a link of a death to waiting time.
"When I was head of the Northern Trust I was told if you didn't meet targets then heads would roll and I constantly replied that the targets could not be met because we didn't have the resources.
"What is needed is beds and they have been taking beds out of the service for the past 10 years.
"We need beds to take people out of the emergency department, we need the staff, we need people to be able to see their GP out of hours and we need minor injury units to be able to deal with people better in order to reduce the amount of people going to the emergency department."
The doctor at the Royal who speaks for the British Medical Association says its members at the hospital have been regularly highlighting how bed shortages mean the emergency department is choked with patients who need to be in wards.
Sara Hedderwick told UTV: "Our members feel that patients are not moving through the hospital and you end up with the wrong people staying in the emergency department instead of being sent to the wards to be looked after which is impacting on the level of care for all and our members feel is harmful."