Arlene Foster and Michelle O'Neill have insisted they have "unity of purpose" over how to contain coronavirus.
Concerns were raised last week after the First and Deputy First Ministers clashed over which businesses could stay open.
At the daily briefing for the Stormont Executive yesterday, it was confirmed that 22 people have now died from coronavirus in Northern Ireland, with 533 confirmed cases.
A total of 54 people have died in the Irish Republic and there have been 2,910 confirmed cases.
Asked about tensions in the Executive, Ms O'Neill said there was "a difference of emphasis" on the best methods, but all five parties shared the same common goal of saving lives.
"When there's disagreement in the Executive (it's often) painted as an Orange versus Green, Sinn Fein versus DUP, London versus Dublin," she said.
"Can I say very clearly that's not the case, this is about what is the best action at the right time.
"How do we save lives? This is about adhering to the World Health Organisation's advice."
Mrs Foster added: "We all have a unity of purpose, which is to flatten the curve of infection so that less people have to be hospitalised and that the NHS will be able to deal with what is presented to them."
The latest progress, she said, included publishing a list of businesses which should close or stay open using strict social distancing measures.
She added that a forum representing business leaders, the PSNI, trade unions and others had met and would bring their concerns to the Executive.
She also warned that businesses who did not follow the rules would face "robust action" including the threat of closure.
"To those who are dragging their feet we say the time for excuses is long past and the community and this executive expects you to take action," she said.
"As Covid-19 wreaks havoc we don't have the luxury of time, and please, please don't unnecessarily place your staff and the wider public at risk."
Asked about whether Northern Ireland would need to build a field hospital, such as the Nightingale Hospital in London, she said the Health Minister Robin Swann was still reviewing the situation.
Ms O'Neill said many families were facing "harrowing" times as the virus spreads.
"I want to send my sympathies to those families who are bereaved at this time, and I think we all need to take a minute just to think about those people who are bereaved through this disease and what they're going through at this terrible time," she said.
"Not only are they dealing with the loss of their loved one, but their pain is also compounded by the fact that they're not being able to grieve in ways which they normally would."
These include people not being able to be with loved ones when they died or attend a funeral. "This is the sad but painful reality of what we're dealing with. Unfortunately this is real life for us all now and the actions of each and every one of us matters."
She added: "Saving lives is the number one priority for the Executive in this crisis. And through this unity of purpose, shared leadership and collective responsibility we are taking action every hour of every day to deal with what is an unfolding situation."
This included a "comprehensive" public information campaign as well as Executive ministers working over the weekend to agree regulations and an enforcement regime. Ministers from Stormont and the Irish Government are also to meet today to agree common practices.
Meanwhile, the Department of Health said the expansion of Primary Care centres for coronavirus in Northern Ireland was continuing. Last week the first GP-led centre opened in Londonderry with more opening yesterday in Belfast, Dungannon and Banbridge. Further centres are set to open this week in Antrim, Coleraine, Newtownards, Lisburn, Downpatrick and Enniskillen.
The centres have been "rapidly established" in each Trust area to help ease the pressure on GPs.
This allows patients with symptoms to be separated from those with non Covid-19 related conditions.
A statement from the Department said the measures were "essential" to allow GP services to function in the coming months.
It was explained the centres are not testing, but for unwell patients with suspected coronavirus symptoms who require medical attention.
Patients are not allowed to attend unless they have been referred by their GP. Those attending will receive treatment and will be sent on to hospital if necessary.