The Scottish First Minister said she has spoken to the MP, who had the SNP whip withdrawn after the incident emerged, and “made clear my view that she should step down”.
Ms Ferrier admitted she was tested for coronavirus on Saturday after developing symptoms but still took a train to Parliament on Monday when she should have been self-isolating.
She gave a four-minute speech in the House of Commons at 7.15pm on Monday during a debate on coronavirus.
I’ve spoken to Margaret Ferrier and made clear my view that she should step down as an MP. I did so with a heavy heart - she is a friend & colleague - but her actions were dangerous & indefensible. I have no power to force an MP to resign but I hope she will do the right thing.
— Nicola Sturgeon (@NicolaSturgeon) October 2, 2020
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The same evening, Ms Ferrier said she received her positive test result – although it is not known if this was before or after speaking in Parliament. She then travelled back to Glasgow.
Ms Sturgeon has now joined mounting calls for Ms Ferrier to resign as an MP over her “dangerous and indefensible” actions.
She tweeted: “I’ve spoken to Margaret Ferrier and made clear my view that she should step down as an MP.
“I did so with a heavy heart – she is a friend & colleague – but her actions were dangerous and indefensible.
“I have no power to force an MP to resign but I hope she will do the right thing.”
SNP Westminster leader Ian Blackford said Ms Ferrier’s position as an MP is untenable following the “tremendous error of judgment”.
He said Ms Ferrier’s SNP whip was withdrawn on Thursday morning when the party learned of her breaches of coronavirus rules.
He told BBC Radio Scotland’s Good Morning Scotland programme Ms Ferrier must now “reflect on the circumstances that she is now in” and “do the right thing for her constituents”.
Asked if he is calling for her to resign, Mr Blackford said: “I would say to her that her position isn’t tenable, given the circumstances that we’re in, and she has to accept her own responsibilities of what she must do. I can’t force that upon her, she is no longer an SNP MP.
“I’m pretty angry at what has happened, it is not acceptable.
“It’s important that it is beyond reproach that everybody, absolutely everybody, must obey the rules and we have to think about the signal that gives the public and the sacrifices that people are having to make, and it’s in the light of that that Margaret will have to do the right thing.”
Statement: pic.twitter.com/rdWYhIauYv
— Margaret Ferrier MP (@MargaretFerrier) October 1, 2020
A number of other SNP MPs, including David Linden whose Glasgow East constituency neighbours Ms Ferrier’s, have also called for her to quit.
Ms Ferrier, the Rutherglen and Hamilton West MP, said she took a test on Saturday afternoon after experiencing “mild symptoms”, meaning she should have self-isolated.
In a statement, she said she travelled home to Glasgow on Tuesday, where she has been self-isolating ever since.
She apologised for her actions and said there was “no excuse”.
Police Scotland said the MP informed them of her behaviour on Thursday and officers are “looking into the circumstances” along with the Metropolitan Police.
She could face a £4,000 fine for a first-time offence of coming into contact with others when she should have been self-isolating, under a law that came into force on the day of her positive test.
UK Communities Secretary Robert Jenrick told BBC Radio 4’s Today programme: “Margaret Ferrier has accepted that she has broken the law.
“That’s now a matter for the police, the authorities who are investigating the matter, and it is really for her to consider what her political future is, and for her party, the SNP.”
Scottish Conservative leader Douglas Ross branded Ms Ferrier’s decision to travel between London and Glasgow on a train with coronavirus symptoms as “reckless and dangerous”.
Mr Ross himself resigned as a Government minister over his party’s refusal to condemn Number 10 aide Dominic Cummings’s trip to Durham with his family at the height of lockdown while suffering coronavirus symptoms.
He said Ms Ferrier’s position is now “completely untenable”.
“No-one can take what she says with any credibility because she has flouted the rules at every opportunity when she first became aware of the symptoms back on Saturday,” Mr Ross said.
SNP in chaos & appear to be covering up serious breach of public health laws. FM & Blackford must hold press conference tomorrow am to answer questions about what they did & didn’t know. Speaker contradicts SNP story. There can’t be 1 rule for the SNP, another for the rest of us.
— Ian Murray MP (@IanMurrayMP) October 1, 2020
Meanwhile, shadow Scottish secretary Ian Murray demanded answers from Ms Sturgeon and Mr Blackford.
The Labour MP tweeted: “SNP in chaos & appear to be covering up serious breach of public health laws.
“FM & Blackford must hold press conference… to answer questions about what they did & didn’t know.”