The Northern Ireland Executive is to meet on Thursday to discuss extensive coronavirus measures as case numbers rise in many areas.
First Minister Arlene Foster said the Executive may have to take similar interventions like those imposed in Glasgow, where households are banned from visiting others indoors.
The Department of Health said 607 people have tested positive for Covid-19 in the last seven days in Northern Ireland.
Another 49 were diagnosed in the most recent 24-hour period, according to the latest daily figures.
There were no further deaths.
The DUP leader said she does not want to reintroduce widespread lockdown measures.
“We want to take proportionate action and we will always have to under the law,” Mrs Foster added.
“We will have a full discussion on Covid. You have seen limited lockdowns in other parts of the UK and the Republic, we haven’t had to do that thus far, we may have to do that tomorrow.”
Ms O’Neill said the Executive will be guided by public health advice.
“The fact that we have data that brings you right down to the postcode level shows that we are able to adapt in a smaller geographical area where we need to,” she added.
“I think it’s inevitable that we will be moving very quickly to local lockdowns that’s going to be required in order to protect people.”
Mrs Foster also said she hopes to give an indicative date for the reopening of so-called “wet pubs” on Thursday.
She said a rise in Covid-19 cases is connected to household transmission.
The DUP leader praised the hospitality sector for how it has implemented the latest health measures.
“Having been out and about, I have been very impressed in the way in which the hospitality sector have been able to mitigate against Covid-19, and restrict movement but yet offer a service,” Mrs Foster said.
“I think it is unfair that one section of one part of our economy have not been able to open.
“I hope that we can give an indicative date tomorrow to those wet pubs.
“They deserve it and people have been abiding by the law for a very long time and I want to pay tribute to their resilience, but I think we do need to give them, in a graduated way, a date they can reopen.”
