The DUP gave a cautious response after Prime Minister Boris Johnson said life in the UK could significantly return to normal by late autumn "at the earliest" with any outstanding lockdown restrictions reviewed at that stage.
The Prime Minister yesterday at a Downing Street press conference announced new measures to tackle the pandemic and further ease restrictions in England.
These include indoor performances with live audiences resuming from August 1 in the region, with trials beginning for sports stadiums, with supporter and spectators in attendance, to reopen from October.
Trials include the World Snooker Championship in Sheffield from July 31 and the Glorious Goodwood horse racing festival from August 1.
Nightclubs and soft play areas, however, will have to remain closed, added Mr Johnson.
The Executive has yet to give indicative dates on when major sporting events will be allowed to go head here.
It comes as 10 GAA clubs in Co Londonderry suspended all activity after Covid-19 cases were detected in the local community.
Last night the DUP appeared reluctant to put a timescale on when the lockdown will end completely.
Sir Jeffrey Donaldson told the Belfast Telegraph that progress on continuing to ease the restrictions will depend on the public carefully following guidance issued by the Executive.
"We want to see progress continue in Northern Ireland and will support easing of restrictions as quickly as is safe to do so," he said.
"Everyone will want to see this happen as quickly as possible, but it will require continued support from the public and adherence to the guidance issued by the Executive."
The Prime Minister's prediction that the UK could return to normality by Christmas was also met by scepticism by the Welsh First Minister Mark Drakeford, who described it as a "pretty sunny view of circumstances".
Mr Johnson, who scrapped advice for the public to avoid public transport in England, outlined plans to focus on extinguishing local coronavirus outbreaks to prevent another national shutdown.
"It is my strong and sincere hope that we will be able to review the outstanding restrictions and allow a more significant return to normality from November, at the earliest, possibly in time for Christmas," he added.
However, the relaxation of the strict rules will require mask wearing and social distancing remaining essential parts of life for now.
The Prime Minister also said yesterday that it will be up to employers in England to discuss with workers whether it is safe to return from August 1.
Mr Johnson's stance pits him against his chief scientific adviser Sir Patrick Vallance, who earlier said there is "absolutely no reason" to change the advice.
But the Prime Minister told his Downing Street press conference: "It is not for Government to decide how employers should run their companies and whether they want their workforces in the office or not - that is for companies."
The Conservative leader announced a £3bn package for the health service in order to help England prepare for a possible second wave.
Other financial packages are expected to be unveiled for the regions, including Northern Ireland.
Health Minister Robin Swann welcomed the investment, saying it will help overhaul health services here, but stressed it will be for the Executive to decide how the additional funds will be allocated.
"While any additional money for Northern Ireland is to be welcomed, it will be for the Executive to decide how it is allocated," he said last night.
"Health and Social Care services continue to face very significant financial pressures. While this was already the case at the start of this year, the situation has been seriously exacerbated by the Covid-19 pandemic."
Mr Swann added: "I will continue to press the case for sustained long-term investment in Health and Social Care."
It comes after the Chief Medical Officer Dr Michael McBride told the Belfast Telegraph this week that medics here were looking for innovative ways to deal with influenza vaccinations as Northern Ireland prepares for a potential second wave of coronavirus this winter.
With the flu season just months away, Dr McBride had said "nothing is off the table in terms of the flu vaccine campaign".
"We can't be bringing older, vulnerable people into a GP surgery. We're actively looking at innovative means of administering the vaccine," he said.
"That could involve outdoor administration or drive-through flu vaccination points."
Mr Johnson also committed to a new target of reaching the capacity for 500,000 coronavirus tests a day by November in order to distinguish between flu and Covid-19 symptoms, and to rolling out the "biggest ever flu vaccination programme".
The Prime Minister warned that the rise in the number of people with coronavirus-type symptoms due to seasonal illnesses could make the job of tracking the virus harder in colder months.
"We're making sure we're ready for winter and planning for the worst," he said.