The SNP has claimed that Boris Johnson “risks jeopardising vital public health measures” by retaining Matt Hancock as Health Secretary.
The party has called for Mr Hancock to resign after he was caught kissing a close aide in breach of coronavirus restrictions.
A video of Mr Hancock in an embrace with Gina Coladangelo was published on Friday night by the Sun newspaper, sparking further calls for his departure.
The SNP said there are “very serious questions” for Mr Hancock and the incident cannot “simply be brushed under the carpet”.
Its Westminster deputy leader Kirsten Oswald said: “Boris Johnson risks jeopardising the vital public health measures in place the longer he desperately clings on to his shamed Health Secretary – just like he did with Dominic Cummings.
“The Prime Minister must at long last do the right thing and put his responsibilities to public health first.
“There must be public confidence in those setting the rules and it cannot be the case that it is one rule for the Tory elite and another for the rest of us.
“Despite declaring the matter closed, the reality is that it is anything but closed.
“There are very serious questions for Matt Hancock to answer over the appointment of his aide to the lucrative position, as well as questions over whether or not Hancock broke the ministerial code.
“This cannot simply be brushed under the carpet.
“The Prime Minister must remove the Health Secretary from his position immediately, and there must be a full independent public inquiry into Tory sleaze and cronyism without any further delay.”
In a statement on Thursday, Mr Hancock said: “I accept that I breached the social distancing guidance in these circumstances, I have let people down and am very sorry.
“I remain focused on working to get the country out of this pandemic, and would be grateful for privacy for my family on this personal matter.”
A Downing Street spokesman said Mr Johnson had accepted Mr Hancock’s apology and “considers the matter closed”.
The Covid-19 Bereaved Families For Justice group, which represents those who have lost loved ones to the pandemic, also called for Mr Hancock to go.
In a letter to the Prime Minister, the group said it has broken its “position of neutrality on ministerial conduct” to urge Mr Johnson to relieve Mr Hancock of his job.