Arlene Foster and Michelle O'Neill have announced that garden centres and recycling centres can reopen on Monday.
Further measures to gently move Northern Ireland out of lockdown are likely to be announced next week.
Marriage ceremonies when a partner is terminally ill are also to be allowed.
The First and Deputy First Ministers made the announcement yesterday after an Executive meeting.
Mrs Foster said that the R number - the rate of the spread of coronavirus infection - had now fallen below 0.7, which made "very tentative first steps" towards recovery possible.
She said: "The Executive met today to assess where we are in terms of our battle against Covid-19 and to consider what restrictions might be lifted as we start to move towards recovery.
"On the basis of the latest scientific and medical advice, the Executive has approved the following measures: from next Monday, garden centres and ornamental plant nurseries will be allowed to open their doors to customers, of course with the proper social distancing measures in place.
"Ministers are also content that household recycling centres should be open to the public and that the disposal of household waste at those sites should be added to the list of what constitutes an appropriate reason for travel.
"Finally, the Executive has agreed that marriage ceremonies for the terminally ill should be allowed to proceed for couples where one of the party or close family member has only a short time left.
"Delaying the marriage is not really an option and we very much recognise that today. We just felt it was wrong that it couldn't happen."
Mrs Foster said ministers had authorised that move after being contacted by a Banbridge woman whose terminally ill cousin wanted to get married.
The First Minister said that the Executive was trying to be "open and transparent" with the public, and would publish the matrix behind its decision-making on the Department of Health website.
"It is important that everyone understands that the process of relaxing restrictions will be incremental and there won't be a dramatic shift," she added.
The coronavirus death toll rose to 454 in Northern Ireland yesterday after a further five fatalities were announced.
The coronavirus death toll has risen to 1,506 in the Republic after a further 10 deaths were announced yesterday.
Mrs O'Neill said: "The changes to the restrictions that we have agreed today have been considered in detail and have been informed by scientific and medical advice. We must remember that the regulations are in place to save lives and the Executive does not take decisions on whether to maintain, or indeed to relax the restrictions, lightly."
The Deputy First Minister stressed that the Executive's advice was that people who have been told to shield at home by the NHS must continue to do so for 12 weeks.
She promised that when the message changed, it would be swiftly communicated.
Mrs O'Neill repeated her call for "universal testing" in care homes. The Deputy First Minister said the Executive will hold further discussions next week about potentially lifting some other restrictions as part of the first step of its five step roadmap out of lockdown.
"These are gradual, small baby steps we are taking," she added.
"Hopefully today is a little step or a glimmer of light for people."
However, she stressed that there was "no room for complacency".
Meanwhile, childcare providers were encouraged by the Education Minister Peter Weir and Health Minister Robin Swann to apply for the Executive's £12m package of measures to support the sector.
Application forms for the Covid-19 Childcare Support Scheme and the Bespoke Approved Home Childcare Scheme have already been issued.
Mr Weir explained: "We established the Covid-19 Childcare Support Scheme to enable childcare providers to meet the needs of key workers and vulnerable children at this very difficult time and to provide support to daycare and school age childcare settings, which are not able to remain open."
The minister added: "I know that it is essential that we get financial support to settings and to childminders without further delay and we are committed to doing that."