Mr Swann took the step after receiving legal advice from Attorney General Brenda King which highlighted potential legal complications of him acting without the wider endorsement of an Executive.
Mr Swann sought the guidance following the resignation of first minister Paul Givan last week, which also removed deputy first minister Michelle O’Neill from the joint office.
While the remaining ministers are still in post, they are unable introduce any new business, and can only progress work already in the system.
The Covid-19 regulations are not due to expire until March 24, but were previously reviewed by the Executive every three weeks.
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Executive approval is ordinarily required for decisions that are significant, controversial or cross cutting.
A letter sent by Mr Swann to other ministers, seen by the PA news agency, said he would now assess whether his proposals to replace restrictions with guidance cross those three thresholds.
His letter stated: “As part of my own consideration, I want to seek colleagues’ input as to whether any or all of these changes should, in your view, be considered to meet any of these three tests.
“It may be the case that I have the power to amend some, but not all of the restrictions without reference to the Executive, because they do not, individually meet the threshold for one or more of these criteria.
“In which case, I believe it may be appropriate to consider where it may be possible to act at this stage, even if I am not able to make a decision in respect of all of the remaining restrictions.”
Meanwhile, former deputy first minister Michelle O’Neill said there is a “real prospect” that Covid restrictions may have to remain in place in Northern Ireland following the legal advice received by Mr Swann.
However, DUP leader Sir Jeffrey Donaldson has insisted that Mr Swann does have the legal authority to remove the restrictions and said it does not need to be a collective decision.
Speaking in Belfast, Ms O’Neill said: “I am aware now that the health minister has received that legal advice and he wants to give it a bit more consideration.
“I hope that we will be able to find a way forward, something which gives the public some hope and some progression in terms of the Covid restrictions.
“This is the direct consequence of the DUP stunt last week, them walking away whenever the rest of us are trying to deal with the pandemic.
“This is the outworking of what the DUP have done.”
Asked about the prospect that the remaining Covid restrictions may remain in place, she said: “We have to see the legal advice, but of course that is a real prospect, this is the outworking of the DUP’s antics.”
She said the Stormont parties would try to find ways to lift the remaining Covid restrictions.
She added: “I would say to people Robin Swann as Health Minister will have my full support, backed by the medical opinion.
“If we can lift restrictions then that is what we should do.
“We have always said we wouldn’t keep them in place for longer than necessary.
“The pandemic has been so challenging on so many fronts.
“If now is the time to lift them, then we will try to find ways to lift them.”
But speaking in Co Down, Sir Jeffrey said: “The Health Minister does have the legal authority to take decisions on this matter.
“The advice he has been given is that he should consult with other ministers before taking decisions.
“There is no suggestion, as far as I understand it that this needs to be a collective decision.
“The Health Minister will consult with other ministers and I hope that happens quickly.
“We support the further easing of Covid restrictions and frankly the sooner that happens the better.”
On Thursday afternoon, Mr Swann confirmed he has received “detailed legal advice on the factors that need to be considered when seeking to amend Executive Covid regulations in the absence of an Executive”.
He added: “This advice is now being given careful consideration and it is my intention to engage with ministerial colleagues.”
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