First Minister Arlene Foster said yesterday that the "shared effort" being made by the public in the fight against Covid-19 was "turning the tide" on the virus.
Mrs Foster said people could take "a degree of hope" from the fact that there is "a slowing in the rate of infection albeit still at a high level".
Speaking at the daily Stormont press conference, the DUP leader said on average, there were 1,000 new cases of coronavirus being recorded in Northern Ireland every day.
"Advisers are optimistic we might reach the point soon where cases begin to fall," she said.
Covid-19: Who will have final say on a way forward?
Ms Foster also said that the the peak for hospitalisations linked to the virus was likely to be within seven to 10 days.
She said the approach going forward should be "built on the foundation that the virus will be with us for some time ahead, but that society must be able to co-exist with it".
In order to do this, she said hospital capacity in Northern Ireland should be increased and the test and trace system improved.
Junior Minister Declan Kearney said there was "already evidence that restrictions are working in Derry and Strabane".
"We are now six days into an emergency four week intervention," she said.
"The restrictions, that we have introduced, are to protect people from the very real dangers of Covid-19. To alleviate pressures on the health and social care system and crucially to save lives."
He added: "The success of our collective efforts in the next three to four weeks in suppressing the virus will depend on a real authentic whole of government and whole of public approach".
Meanwhile, Economy Minister Diane Dodds announced further financial support for businesses without premises that have been those forced to close.
She said the Covid Restrictions Business Support Scheme will provide payments to businesses impacted by the latest restrictions who have not been able to access support.
Running for four weeks, it is aimed at those not eligible for the localised support scheme.
There will be three different payments.
The scheme will also help some very small businesses who were left out of a previous scheme, along with people who acted as suppliers to closed businesses.
Last week, businesses which were forced to close their premises were told they would be eligible for grants.
That scheme, set up by the Department of Finance, is mainly based on what business rates they pay.
The executive said that more than 8,000 applications have already been received.
Mrs Dodds said she hoped that her new scheme would open for applications as quickly as possible.
Meanwhile a package of £20-25m is being considered for sporting bodies who may have to play games without fans.
