Nicola Sturgeon has warned it could be “catastrophic” to drop the stay at home message as she announced that the lockdown is to be extended in Scotland.
It has been suggested that Boris Johnson could scrap the slogan as part of moves to ease some lockdown rules.
Ms Sturgeon said the Scottish government may be prepared to allow people to spend more time outdoors.
But she said scrapping the “clear, well understood” stay at home message was “a potentially catastrophic mistake”.
Ms Sturgeon said she would prefer all four nations to make changes together because that would help give consistent messages to the public.
However, she said it was possible to go “different ways” if they were at different stages.
Following a call between Ms Sturgeon and the prime minister, a spokeswoman for Mr Johnson acknowledged that different parts of the UK could “move at slightly different speeds”, with “decisions made based on the science for each nation”.