Stormont's leaders are facing new pressure to take us out of lockdown faster after the Republic accelerated its lifting of restrictions.
A health expert has joined calls from industry to speed up the roadmap back to normality.
It came as statistics showed the Covid-19 death toll here had fallen for the fifth week in a row.
Friday's Northern Ireland Statistics and Research Agency (Nisra) data revealed 36 virus-linked deaths in the week to May 29, down 11 on the previous week.
One further death was also announced by the Department of Health on Friday. However, this occurred on May 30.
Meanwhile, Taoiseach Leo Varadkar announced the Republic's five-phase plan had been cut to a four-phase exit, bringing forward the dates for the reopening of stores and parts of the hospitality industry.
It led to warnings that Northern Ireland will be disadvantaged unless it moves quicker.
TUV leader Jim Allister said the Executive needed to stop "dragging its feet and get on with easing our economy-destroying lockdown".
Former Economy Minister Simon Hamilton, who is now chief executive of the Belfast Chamber of Commerce, said the Republic had taken a "bold" approach.
He warned we were now at risk of lagging behind, adding that the Republic's move would increase pressure on the Executive.
"We're not saying the date here needs to be exactly the same, but they can't allow us to fall behind other jurisdictions like our neighbours in the south," he added.
However, the Executive Office said that while it understands the "damaging effects" of the restrictions, the "priority is still saving lives".
The pressure on Stormont increased in the wake of Mr Varadkar's lunchtime address on Friday. From Monday all retail outlets in the Republic will reopen with staggered hours. Distance restriction on exercise has been extended from 5km to 20km, or any distance within a person's own county boundaries.
It means people here could soon eat a meal in a pub or buy a pair of shoes across the border. Mr Hamilton added: "We're now sitting as a bit of an outlier. England is moving forward with dates for their retail and hospitality, and the Republic is accelerating its original timetable, which is interesting and significant, and highlights the dichotomy on two sides of the border.
"We have dates for some retail to reopen, and hotels, but in the south dates are being brought forward. The contrast is that very soon you can go for a meal in the pub in Dublin, in Donegal or Dundalk, but you can't in Belfast, and you can buy a suit and new shoes in Dublin, but you can't in Belfast."
Hospitality Ulster chief executive Colin Neill said pubs and restaurants also needed the certainty of when they could open.
"With the Government in the Irish Republic announcing that it is bringing forward its dates for when retail and hospitality can reopen, the Northern Ireland Executive urgently needs to follow suit," he insisted.
The Northern Ireland Hotel Federation said it hoped hotels could reopen faster.
They are slated to reopen here on July 20 - the original date set in the south, which has been brought forward to June 29.
"We are aware that this is the wish of hotels in a number of locations who rely on a strong summer season," said its CEO, Janice Gault.
The Nisra figures, which showed 36 deaths in the week to May 29, are less than a third of the 119 recorded in one week at the height of the crisis. They had fallen to 82, 62, 52 and 33 in previous weeks.
It led Professor Karol Sikora, a former World Health Organisation (WHO) expert, to declare the "worst ravages" of the crisis is over in Northern Ireland.
He believes we can now afford to follow in the Republic's footsteps. Prof Sikora said coming out of the lockdown is always a "calculated gamble", but pointed to countries like Austria, Denmark and the Czech Republic, saying they have emerged from restrictions weeks ago without seeing a second wave of cases.
He added: "Northern Ireland has been good about the lockdown. I think you can come out faster."
The Executive Office said: "Ministers understand the damaging effects of the restrictions on people's livelihoods and their health and wellbeing, and have agreed not to keep any restriction in place longer than necessary.
"But the priority is still saving lives and the Executive will continue to be guided by the scientific evidence and medical advice to move through recovery in the safest way possible."