Health Minister Robin Swann has said no hospital will turn away a Covid-19 patient but people with other serious illness may have to wait for treatment.
His comment comes after the Belfast Health Trust chief said the system was facing the “most difficult challenge” she has seen in her 33-year career.
Dr Cathy Jack said having to prioritise some patients over others was leading to “moral distress” for clinicians.
Eleven more Covid-19-related deaths were recorded on Friday.
Another 607 people have tested positive for coronavirus.
Speaking to BBC News NI, Mr Swann acknowledged that people waiting for treatment for other serious conditions such as cancer could suffer further as a result of the pressure on hospitals.
He said: “The ethical decision is could we turn a Covid patient away? The answer is no.
“So where we get the latitude in our current system, with our current staff, is by saying to other people: ‘No, sorry – your operation, your scope, your diagnosis is going to have to be put off until we can safely accommodate you within the health service.'”
Asked if that meant some of those people may die as a result of that delay, Mr Swann said: “Yes, that’s as black-and-white as it is.”
Speaking on BBC Radio Ulster’s Talkback programme, Dr Jack said there were 170 patients with Covid-19 in Belfast Trust hospitals.
“And across Northern Ireland there are 44 critically ill patients in intensive care with Covid-19,” added Dr Jack.
“Over the past three weeks there have been more patients in Belfast Trust who are ill with Covid than in the peak of the first surge.”
Dr Jack said there had been a “huge impact” on the trust’s elective surgical capacity.
“When we talk about elective surgery, I want to point out that many of these patients are very, very, sick and in desperate need of surgery.
“We are not talking about simple procedures – I’m talking about elective surgery like cardiac surgery and indeed some of these patients will have cancer.
“I have the capacity to treat everyone with Covid-19 that needs to be treated but the cost of this is that elective care has been downturned and every day we have to make clinical decisions on who needs the treatment most.
“Now that is something where no nurse, no doctor, no social worker and no manager ever wants to be in.”
Dr Jack said that in regard to people who had surgery delayed “there is potential harm and the outcomes may not be as good as if they had surgery earlier”.
“I need to tell you today about the moral distress that that is causing some of my clinicians and my senior managers where they are having to make decisions that we have never had to make before.”
Asked if those were “life and death decisions”, she replied: “Yes.”
The Belfast Trust chief executive appealed to the public to “play their part”.
“We need to bring this [coronavirus transmission rate] down so that our hospitals cannot only treat those who are critically ill with Covid-19 but also the other patients that are being affected and their care is being downturned,” she said.
“So I’m appealing directly to the public to wash their hands, wear a face covering, but keep their distance, limit their contacts because by working together, and we have seen how successful this can be in the first wave.
“That’s what we need to do now so that our hospitals can open up again as they did over the summer and prioritise other critically ill patients that we need to treat.”
On Thursday, restrictions were extended for one more week with a partial reopening of some sectors due next Friday.
Close-contact services and unlicensed premises can reopen on 20 November.
First Minister Arlene Foster has said she regrets how the Stormont Executive handled the decision over extending Covid-19 restrictions this week.
Dr Jack said she “would not want to be a politician” and added: “They have difficult jobs balancing lives and livelihoods and none of this is easy.”