DUP Economy Minister Diane Dodds is calling on the Executive to fast-track its journey out of lockdown and open shops, cafes, restaurants and bars.
And she is urging it to consider reducing social distancing guidelines here from two metres to one metre so businesses can serve more customers.
A relaxation would also have major implications for public transport and the reopening of schools.
The World Health Organisation (WHO) recommends one-metre social distancing, but the UK and Republic believe two metres is the safest option.
The Executive will discuss the DUP proposal when it meets on Monday morning.
Support for accelerating the easing of lockdown so significantly isn't guaranteed, with Sinn Fein insisting throughout the pandemic that public health must always be the priority over business needs. Alliance, the SDLP and Ulster Unionists are also likely to be cautious.
Mrs Dodds said that the economic consequences of not opening for business would be colossal.
She has written to Health Minister Robin Swann, who is responsible for Northern Ireland's coronavirus regulations. The Department of Health will now order risk assessment modelling.
Chief Medical Officer Dr Michael McBride and Chief Scientific Officer Professor Ian Young are expected to give their views to the Executive before Monday's meeting.
The DUP move comes as the Taoiseach announced a fast-tracking of the Republic's journey out of lockdown, with all shops allowed to reopen on Monday unless they are in a shopping centre.
Mrs Dodds said we had to move more swiftly out of lockdown.
"Every month that passes with significant restraints on trading is the equivalent of a large scale recession," she said.
"Northern Ireland output is at least 25%-30% down. I have never tried to sugar-coat this. I fear that the recovery will not be as quick as the decline.
"The greatest help we as an Executive can provide to people is to allow our economy to function again in a manner that protects both staff and customers.
"On that basis I have requested that the Executive considers allowing the wider retail sector to open up and begin trading again."
The DUP minister said she wanted to see "as much of our economy open as possible".
She added: "Obviously this reopening must be in line with our knowledge about the transmission of the virus and consistent with the medical advice.
"However, as long as shops, cafes, restaurants, bars and attractions can open up in a safe and sensible way then we should move ahead with that phased reopening."
Mrs Dodds said that the Executive had "big decisions" to make on social distancing.
She noted that UK, Irish, US and Swiss government advice was that people should remain two metres apart.
In Germany, the Netherlands and Poland it was one-and-a-half metres. Sweden, Finland, Norway and Austria have adopted the WHO-recommended one metre.
"New research funded by the WHO suggests that keeping one metre apart can reduce the likelihood of catching Covid by some 80%," Mrs Dodds said.
"It is generally accepted that we will be co-existing with this virus for some time. The difference between one and two metres will dramatically impact on workplaces such as a production line on a shop floor or a hotel's ability to hold functions such as wedding receptions, conferences or banquets. Likewise it impacts how many customers a restaurant or bar can safely serve at one time, or how many people can visit a theatre, travel in a bus or sit in a cafe. These are the balance of judgments that the Executive has to make."
Businesses have been pressing for a relaxation of guidelines.
However, a study published this week suggested that moving from two to one metres could significantly increase the risk of infection.
The Lancet study, which reached its conclusions from an analysis of nine pieces of research, put the risk of infection at 3% when people stand more than one metre away, compared with 13% if within one metre.