"And when trust in a public health message and public health advice is asimportant as it is right now the consequences of that could be serious.
"I hope that the Prime Minister will reflect further today and perhaps come toa different conclusion than the one he made yesterday."
Ms Sturgeon said she had a "particular insight" into the situation afterScotland's chief medical officer Catherine Calderwood resigned when photosemerged of her visiting her holiday home during lockdown.
Ms Sturgeon said that Dr Calderwood had not tried to "save her own skin" atthe expense of weakening the lockdown message.
She added: "I put the importance and integrity of the public health messagefirst and to Catherine Calderwood's great credit so did she.
"She didn't try to save her own skin at the expense of the public healthmessage and I think that's what has to happen here now with the Prime Minister and Dominic Cummings."
After the Prime Minister's speech on Sunday night, the First Minister said Mr Cummings should either resign or be sacked. She said: "I know it is tough to lose a trusted adviser at the height of crisis, but when it’s a choice of that or integrity of vital public health advice, the latter must come first," Ms Sturgeon tweeted.
"That’s the judgment I and, to her credit, Catherine Calderwood reached. PM and Cummings should do likewise."
Coronavirus: Everything you need to know