Robin Swann said he did not "want a return to a long-term or indefinite lockdown".
Meanwhile public health experts in the Republic of Ireland have recommended the highest level of restrictions be applied to the entire country.
It is expected politicians will meet the chief medical officer on Monday.
A further 462 cases of Covid-19 were announced by the Department of Health on Sunday.
One person has died in the past 24 hours after testing positive.
There are 65 people in hospital after testing positive for the virus, of whom nine are in intensive care.
In the Republic of Ireland, 364 new Covid-19 cases were recorded on Sunday, with no new deaths reported.
Deputy First Minister Michelle O'Neill said "any notion of a circuit breaker only works if it's across the Island of Ireland".
The executive's Chief Scientific Advisor, Prof Ian Young, said "other levers are likely to be needed" in addition to NI-wide restrictions on household gatherings.
In a statement issued on Sunday evening, he said the hospitality sector was the "second most important" for interventions "to reduce adult contacts".
He said contacts in this sector "tend to be closer and longer" than in many other settings, while alcohol consumption "will also be a factor in failure to comply with social distancing".
Prof Young added there had been a "number of identified clusters associated with the hospitality sector", however, minister will have to weigh up measures "while also seeking to mitigate adverse consequences for society and the economy".
Earlier, Stormont Finance Minister Conor Murphy told BBC's Sunday Politics that "all options" would be discussed when the executive meet on Monday.
Meanwhile, a 46-year-old woman has been charged with breaching coronavirus regulations in Strabane.
The woman is the first person in Northern Ireland to be charged under the new legislation.
She is due appear at Londonderry Magistrates' Court on Monday.
Mr Murphy said he was "concerned" about the rising cases, adding "as are all of the executive".
"The primary focus of the executive is to protect life and whatever steps have to be taken we will take them," he said.
"We have to take a balanced view and one which we are sure the population will come along with us."
Robin Swann said NI's hospitals were "already under growing pressure and this will intensify in the coming weeks given the extent of the new cases".
"Concrete action has been taken by the executive on a number of fronts and I will not hesitate to recommend further restrictions," he continued.
"Saving lives and protecting our health service must come first."
The health minister also urged people not to "look for loopholes or grey areas in the regulations".
New restrictions for the Derry City and Strabane Council area were announced by the Stormont executive on Thursday in an effort to stem spiralling infection numbers.
They include hospitality businesses being limited to takeaway, delivery and outdoor dining, and a call to avoid unnecessary travel.
Speaking about the rise in cases across NI, Dr Gerry Waldron of the Public Health Agency said a circuit-breaker lockdown was "almost inevitable".
A circuit breaker is a short, sharp period of tightened restrictions for everyone to curb the spread of coronavirus.
"It's not a place we expected to be at this time of the year, at the beginning of October, we thought, if anything, we might be seeing that maybe middle of October," he told Radio Ulster's Sunday with Steven Rainey show.
"We are absolutely insisting that people follow the advice of maintaining a social distance from other individuals, as far as possible, of two metres.
"We'll just have to brace ourselves and see how things pan out over the next few days and the next week."
He stressed the need to stick to the basics - keep a social distance, wear a face mask and keep washing your hands.
Speaking on the BBC's Andrew Marr show, Boris Johnson urged people to behave "fearlessly but with common sense" in their approach to the coronavirus.
The prime minister warned of a "bumpy ride" until Christmas and beyond, saying the winter could be "very tough" for everyone.
He added there had to be a balance between saving lives and protecting the economy.