First Minister Arlene Foster says there has been "significant progress" following three weeks of further restrictions with a drop in the number of cases, and the reproductive rate of the virus has dropped to around 0.7.
Speaking at a briefing held at Stormont she said the number of patients with coronavirus requiring treatment remained high and the proportion of older people affected had increased.
Mrs Foster said Stormont ministers had held a "comprehensive discussion" about what to do when current restrictions on hospitality expired on November 13.
Medics have recommended their extension.
She said: "These discussions will continue and we will intensify our engagement with the hospitality sector representatives as we seek a safe and sustainable way forward."
Mrs Foster said the Executive considered a "range of medical and scientific" evidence at a meeting today.
She said there has been "significant progress" following three weeks of further restrictions with a drop in the number of cases, and the reproductive rate of the virus in the community has dropped to around 0.7.
"The chief scientific adviser has indicated that for our local government districts, a majority of council areas have already reached rates of 0.7 or below," she said.
"However the number of patients requiring treatment in our intensive care units remain high and the proportion of older people contracting Covid has been increasing, so there is still more to do to ease pressure on our health service and to save lives.
"We have one week to go with our current restrictions and we are asking people to redouble their efforts."
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Mrs Foster said Economy Minister Diane Dodds has advised that the four-week circuit-break restrictions will cost the local economy £400 million.
She welcomed the extension of the furlough scheme which was announced today by British Chancellor Rishi Sunak. Read more
"The Executive has had a comprehensive discussion this afternoon on what measures may need to be introduced from November 13 when this current package of enhanced restrictions come to an end," she said.
"Those discussions will continue and we will intensify our engagement with the hospitality sector representatives as we seek a safe and sustainable way forward for that industry.
"We want to be able to make announcements at the earliest possible opportunity to provide businesses with certainty and allow people to see the plan."
Deputy First Minister Michelle O'Neill described an appeal by Rhonda Tait whose mother died in April as a "powerful reminder to us all about just how devastating this virus really is".
"Her grief is still very raw but she has found the strength to come forward to tell her story in the hope that others will be spared that same pain," she said.
Ms O'Neill expressed her concern that 409 people are currently in hospitals with Covid-19, more than at any point during the first wave of the virus.
Coming at the same time as "significant levels of staff absences across the system", she described the situation as "simply not sustainable".
She said health staff need help.
"The infection rate won't stay at a low enough level unless we work very hard to keep it there," she said.
"Our objective is to keep the transmission rate as low as possible for as long as possible. We appeal to everyone to be patient, to work with us in the weeks and months ahead.
"We're in for a difficult few months, there is also some room for hope, let's keep our sights on the springtime when we're hopeful we are going to have an effective vaccine."
