He was speaking at the first Stormont press conference on Tuesday afternoon to take place in more than six weeks after a row between the DUP and Sinn Fein over the Bobby Storey.
On Tuesday, one more death was recorded bringing the Department of Health’s death toll to 559.
Mr Swann warned that the North of Ireland was in danger of “sliding down a very slippery and treacherous slope”.
Forty-one new cases of coronavirus have also been recorded by the Department of Health, bringing its total to 6,471.
One of those cases was in the Derry City and Strabane District Council area which has so far recorded 29 deaths.
NI’s Chief Scientific Adviser Prof Ian Young said officials were seeing an indication of an increase in hospital admissions, but that they remained at a “low level”.
“If cases continue to rise it’s inevitable hospital admissions and deaths will rise in the future,” he told the press conference.
Almost 300 new cases have been confirmed in Northern Ireland over the past seven days.
Mr Swann warned that people needed to realise the virus was still present in Northern Ireland.
“It is not inevitable, we can still arrest that slide but this requires decisive action from all of us,” he added.
“COVID-19 won’t go away just because we are fed up with it.”
The minister said he wanted to “address doubters and critics” who had accused him of exaggerating the threat posed by the virus.
“They’ll say infections are mainly impacting young people – this argument overlooks the fact there can be a time lag between infection and people becoming ill,” added Mr Swann.
He said there were always fine judgements to be made, but warned that the executive would soon need to consider the next steps in a bid to stop the virus from spreading more widely within the community.
“The time is coming for the executive to consider fresh and concrete actions to prevent further spread of the virus,” said the minister.
“This could include imposing localised restrictions or general measures or a combination of both.
“Given where we are now, Thursday’s executive meeting will have important decisions and options to consider.”
The executive has to regularly consider the coronavirus lockdown restrictions, the latest of these being due to take place in two days’ time.
The North’s Chief Medical Officer, Dr Michael McBride said he did not want anyone to be in a position to reflect in the future and think they should have done more or “listened more carefully to the advice”.
He said the executive could need to look at restrictions on the number of people gathering outdoors.
“If indeed we see particular clusters related to particular establishments such as pubs or restaurants those also may be things we need to look at,” he added.
During Tuesday’s press conference, Mr Swann also said the Department of Health’s contract tracing app for COVID-19 had been downloaded almost 276,000 times so far.
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