After the bluntness of the shutdown message "stay at home, save lives, protect the NHS", Britons are now to be asked to "stay alert, control the virus, save lives".
Communities Secretary Robert Jenrick said a "broader" slogan was needed as the Government tries to restart the economy.
"I think that's what the public want and that they will be able to understand this message, which is that we should be staying home as much as possible but when we do go to work and go about our business we need to remain vigilant, we need to stay alert."
Asked on Sky's Sophy Ridge On Sunday if there was a danger the message was too woolly, Mr Jenrick said: "Well I hope not.
"We need to have a broader message because we want to slowly and cautiously restart the economy and the country."
But Scotland's First Minister Nicola Sturgeon said she would not be ditching the current "stay home" message.
"The Sunday papers is the first I've seen of the PM's new slogan.
"It is of course for him to decide what's most appropriate for England, but given the critical point we are at in tackling the virus, #StayHomeSaveLives remains my clear message to Scotland at this stage."
Shadow health secretary Jonathan Ashworth said: "I think the problem with the slogan that has been briefed to some newspapers is that people will looking at it slightly puzzled, questioning what does it mean to stay alert and what are the government saying with that."
He also criticised selective briefings about the new message ahead of the Prime Minister's address to the nation on Sunday evening, saying it had confused the public.
"I think some of those briefings to newspapers has led to the situation yesterday and on Friday of lots of people going to parks, enjoying the sunshine."
Andy Burnham, the Labour Mayor of Greater Manchester, tweeted that it "feels to me like a mistake to me to drop the clear" stay at home message.
Dave Ward, general secretary of the Communication Workers Union, said: "The messaging from this Government throughout this crisis has been a total joke, but their new slogan takes it to a new level."