First Minister Arlene Foster has said there is a "unity of purpose" among the executive to save lives.
She was speaking after Deputy First Minister Michelle O'Neill criticised the response of the Department of Health to the crisis.
At the daily Stormont briefing, Ms O'Neill also stressed that ministers were working together.
A total of 48 people have died with coronavirus in Northern Ireland, with 904 confirmed cases in the region.
Mrs Foster highlighted the fact that a surge in cases was expected between 6 April and 20 April.
She said it was very important that "regardless of all of the other bits of noise", public health messages still got out.
Mrs Foster added: "So be under no illusion and let me say again, we are very much united in that unity of purpose in saving lives."
She added: "Whilst it may be tempting for some people to concentrate on apparent inconsistencies of approach between jurisdictions or indeed executive ministers, we need to focus on the things that really matter and we need to focus on getting our hospitals tooled up for the very difficult days ahead, of ensuring our nurses, doctors or indeed other key workers have the kit they need."
Ms O'Neill said that people were facing the "battle of our lifetimes".
"I am doing everything in my power, and we are, to make sure that we win that fight, to make sure we come out the other side of this as best as we can.
"This isn't about politics, this is about doing right by our people, we're looking into the peak of the first wave of this pandemic over the course of the next number of days and everything we do has to be, and is always about, saving lives, everything comes back to that.
"The executive's priority is to save lives."
Health Minister Mr Swann, who also took part in the briefing, declined to respond to Ms O'Neill's criticism.
He said: "My skin's thick enough to take whatever abuse anybody wants to throw at me, because I'll not be distracted from the work that we're doing, I'll not be allowing my department to be distracted from the work that it's doing.
"Because we've done a lot of good work in a very, very short space of time - so we'll keep doing what we're doing."