Mr Swann said the progress made since March should not “be taken as a sign that COVID-19 is over or finished”.
He said: “If we get this wrong now, if we don’t keep our controls in place, if we don’t see the people of Northern Ireland actually respecting the guidance and regulations we are asking them to, we could see a further increase of COVID outbreaks, more hospitalisations, more people going into ICU, and unfortunately more deaths”.
Mr Swann said that is something he nor “anyone in Northern Ireland wants to see”.
He said NI’s test, track and trace system is working well.
Said the Health Minister: “But my concern is that complacency is setting in now.
“We have seen the relaxations we have been able to put in place over the last two to three months.
“But we are starting to see people, I think, taking a step back even from some of the basic guidance we were putting out”.
He said that includes hand washing, mask wearing, and social distancing.
Mr Swann added: “Those are all there for a reason. I am asking people in Northern Ireland to reengage with the guidance so we can prevent a serious increase in the number of cases in the coming weeks and months.”
On Tuesday, the Department of Health reported that there had been 48 more positive cases from Coronavirus in the North of Ireland in the previous 24 hours.
There had been no further deaths but there are concerns that there is now a steady rise in positive cases since lockdown measures were eased.
The chairman of the British Medical Association NI GP Committee has said the recent rise in positive cases in the North of Ireland is a “wake up call for us all”.
Dr Alan Stout said “the virus hasn’t gone away” and this increase in cases was something that was “anticipated”.
“Once we started to open everything up, people started to interact and go out we always knew there would be small spikes of the virus,” Dr Stout said.
“What this is doing at an early stage with increased numbers is really giving us a warning.”
Dr Stout said it was imperative that people continue to follow all public health guidance.
“Regular hand washing, social-distancing, good respiratory hygiene and the wearing of masks in public settings and indoor settings in particular”.
Health chiefs continue to ure the public to maintain a social distance of two metres as much as possible, to wash hands regularly and often, and wear a face covering in shops and other enclosed spaces to prevent the spread of the deadly virus.