Small shops in Northern Ireland can open on Friday, with the Executive set to announce the future for pubs, cafes and restaurants later this week.
Arlene Foster and Michelle O'Neill said the latest scientific advice gave "head room" for fast-tracking the journey out of lockdown as there were no deaths from coronavirus here for the second day in a row.
It's only the third time that no Covid-19 deaths have occurred in a 24-hour period since the first case here in March. Our death toll stands at 537 people.
The Executive will meet to consider the way forward for the hospitality and tourism sectors on Thursday when a date for the reopening of bars and restaurants is expected.
Mrs Foster said that, while saving lives remained a priority, the Executive was now also focussing on saving livelihoods.
"The coronavirus pandemic has had a devastating impact on our economy and wider society," she said during the daily press briefing at Stormont on Monday.
"The longer people are removed from the labour market, the greater the risk of long-term scarring on our economy and wider society.
"We need to take action to help the economy recover and this will be gradual and in stages."
She was speaking just hours after DUP Economy Minister Diane Dodds announced that all non-essential retailers, not inside shopping centres, could reopen from Friday.
Ms O'Neill said that it was "very positive" that Northern Ireland has had no Covid-19 deaths for two days. It showed that there was a "glimmer of light at the end of the tunnel".
The medical and scientific advice given to the Executive was that there was "some latitude to make further relaxations" regarding lockdown, she said.
Stormont wanted to ease those restrictions which carried the lowest risk but offered the biggest benefit to the economy and community, she added.
The deputy First Minister said it was important to avoid a situation where smaller local businesses were put at a competitive disadvantage.
Allowing those retailers to open was considered "relatively low risk at this time", she said.
The decision will be confirmed when the Executive meets on Thursday.
Ms O'Neill said it would be a "special meeting" to allow ministers to discuss short, medium, and long-term recovery plans.
While saving lives remained the priority, Stormont would not keep restrictions in place any longer than necessary and would maintain a flexible approach.
There would be "strongly held, contrasting views" around the Executive table on the way forward but ministers would continue to do right by the public, she added.
Mrs Foster and Ms O'Neill did not ease restrictions on family members or friends meeting indoors where Covid-19 is more easily spread.
But they said they wanted to explore the social bubble concept, which has been successfully adopted in New Zealand, and allows the same small group of people to meet indoors.
"We are all very mindful in the Executive of the desire of families and friends to meet. We will consider that on Thursday as well," Mrs Foster said.
The First Minister said that the reopening of hairdressers and barbers would have to be considered at a later stage of Northern Ireland's recovery plan due to the close contact involved.
But she announced that a working group, involving the churches and other faith groups, would be set up to discuss how to achieve the gradual reopening of places of worship here.
Ms O'Neill said the Executive was still considering its policy on face masks.
She said that previous medical advice was that while face masks were helpful, they could also give people a false sense of security.
Mrs Foster said there was evidence that those wearing face masks thought they didn't have to engage in other hygiene practices as extensively.
She said she had seen people wearing them who were not social distancing.
The First Minister stressed that face masks didn't protect the wearer, "it only protects others from you breathing upon them".
Announcing the opening of all non-essential retail from June 12 during a visit to Debenhams in Belfast city centre, Mrs Dodds said: "It was agreed that as long as retailers can adhere to the necessary safety measures, and there is no increase in the spread of the virus by Thursday, then these shops can reopen.
"The pandemic has had a devastating impact on the local economy.
"The recovery has already begun and it is time now for the pace to accelerate.
"The reopening of all goods retail outlets will be a huge part of this.
"The safety of staff and customers is of course paramount. All retailers must be able to implement measures that minimise the risk to their staff and to the people who visit their stores.
"We will be co-existing with this virus for some time to come so it is vital that we continue to adhere to guidance to work and live safely."
The UK yesterday recorded 55 new coronavirus-related deaths, the lowest daily total since lockdown began. The UK death toll now stands at 40,597.