The First Minister said Boris Johnson should question whether a trip north was vital during the current Covid lockdown and suggested there should not be different rules for the public and politicians.
Her urging came as it was revealed a second SNP MSP, Kenny MacAskill, had twice broken lockdown restrictions by travelling from his second home in Banff to his constituency seat of East Lothian.
While she stressed she was not saying Mr Johnson was not welcome, Ms Sturgeon said: “I would say me travelling from Edinburgh to Aberdeen to visit a vaccination centre right now is not essential, and Boris Johnson travelling from London to wherever he is [going] in Scotland to do the same is not essential.
“If we're asking other people to abide by that, then I'm sorry, but it's probably incumbent on us to do likewise. I am not and never would be saying that Boris Johnson is not welcome in Scotland – he's the Prime Minister of the UK.
“But we're living in a global pandemic right now. Every day I look down the camera and say ... don't travel unless it is really essential, work from home if you possibly can and that has to apply to all of us.
“Boris Johnson and I have to be in work for reasons most people will understand, but we don’t have to travel across the UK as part of that right now.
“We have a duty to lead by example and if we are going to suggest that we don't take these rules as seriously as we should, it gets harder to convince other people. That's why I'm perhaps not ecstatic about the thought of the Prime Minister visiting, it's not because he's not welcome.”
Current regulations in place by the Scottish Government state that only people making essential journeys across the border are allowed to enter Scotland, in a bid to stop the spread of coronavirus. Similar regulations are also in place to stop travel across council boundaries.
Speaking at the Scottish Government's daily briefing, Ms Sturgeon said the visit was not discussed on the four-nations Covid call, but she was sure the Prime Minister's advisers would ensure he “wasn't breaking any laws”.
She also said she questioned the nature of her own visits.
“In Scotland right now, I'm asking myself ‘is it essential for me to visit a vaccine centre or not?’” she said.
"I would love to go to every IC [intensive care] unit in the country to personally thank those who've done so much for us, but it would not be essential for me to do that right now.”
A spokesperson for Mr Johnson later said it was a “fundamental role” of the Prime Minister “to be the physical representative of the UK Government and it is right he is visible and accessible to businesses and the public in all parts of the UK, especially during this pandemic”.
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