Writing in the Daily Mail, the Scottish Secretary said both Westminster and Holyrood must "present a simple, clear, united message" as plans for lockdown restrictions being eased are formed.
The entire UK entered lockdown at the same time (March 23), but Scotland's First Minister Nicola Sturgeon and the first ministers of Wales and Northern Ireland have reserved the right to alter the current rules at different times to England if they choose.
But Mr Jack firmly believes the different nations of the UK should come out of lockdown at the same time.
He said: "I believe that when Scotland is ready to emerge from lockdown we should do so in lockstep with the UK as a whole.
"There are strong, practical reasons why this should happen.
"It’s important, as Scotland’s two governments make such onerous, difficult demands on people to stay at home and to stay away from family and friends, that we speak with the same voice."
Mr Jack went on to say that if a "simple, clear, united message is presented, it will be much more effective.
"The more we feel we are in this together, the more we will pull together - to stay at home, protect the NHS and save lives," he continued.
Mr Jack added that a UK-wide approach will also be best for Scottish businesses.
"It will help our economy recover as strongly as possible. It will help save as many jobs as possible," he said.
"We are, after all, part of the UK economy.
"Sixty per cent of Scotland’s trade is with the rest of the UK and as we begin to ease restrictions our businesses will need a level playing field to compete.
"So I’m in no doubt that moving forward as one United Kingdom will save lives and save livelihoods.
"I’m glad to say that the UK Government and the Scottish Government are in agreement on that broad principle."
Speaking at her daily briefing yesterday (March 4), Ms Sturgeon said it is "very likely" the Scottish Government will continue lockdown measures beyond a scheduled review on Thursday.
The First Minister said although "real and significant progress" is being made, the rate of reproduction of the virus is still too high to relax lockdown measures.
She said some work on a potential transition from lockdown will be published in the coming days and while work would be done to ensure there is alignment with the rest of the UK, divergence in measures could still be possible.
The First Minister added she wants to be delivering a daily briefing "in a few weeks" saying the measures are being eased.
"My big worry is that if we ease up now then I won't be able to do that," she said.
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