Mr Salmond began the show in November 2017, five months after he lost his Gordon MP Seat at Westminster. The former SNP leader hosts various political and public figures on the show which airs every Thursday on RT’s UK channel.
The demand for her to speak out comes a day after the release of the Intelligence and Security Committee’s (ISC) report on Russian meddling in UK democratic processes.
The report said RT, formerly known as Russia Today, put out “serious distortions” along with fellow “state-owned broadcaster Sputnik”.
The report claims that Russia spreads “disinformation” and runs “‘influence campaigns”, including “use of state-owned traditional media”.
Alongside this, it also said there is “credible open source commentary” suggesting Russia used influence campaigns during the Scottish independence referendum campaign in 2014.
Speaking yesterday, SNP MP and ISC member Stewart Hosie said another Westminster committee had previously recommended the UK Government look into interference concerning the 2014 vote but stressed that Whitehall had ignored the calls.
However, today a Labour Party spokesman said Sir Keir “condemned” Mr Salmond’s appearances on the Kremlin-backed channel.
He said: “We completely condemn it and we advise the First Minister Nicola Sturgeon to do the same. She should make a public statement condemning it.”
“Keir would certainly say it is the wrong thing to do.”
“As Keir said, no member of the frontbench has been on Russia Today since Keir was put in charge and it is certainly not anything we would endorse.”
Scottish Tory MP and former Scottish Secretary David Mundell backed Mr Starmer’s calls, and said: “It is now abundantly clear that the RT network, controlled by the Russian state, is used to disrupt and destabilise other countries.”
Alex Cole-Hamilton, Scottish Liberal Democrat MSP for Edinburgh Western, added: “Alex Salmond needs to accept that he has been promoting a TV channel that has a damaging agenda for western democracy.
“He should pull out now because he is insulting our country’s democratic values by staying in his post.”
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Nicola Sturgeon had previously voiced her uncertainty about Mr Salmond’s choice of channel after announcing the show in 2017 that “the choice of channel would not have been my choice”.
Speaking at the time, she said: “Of course, Alex is not currently an elected politician and is free to do as he wishes, but had I been asked, I would have advised against RT and suggested he seek a different channel to air what I am sure will be an entertaining show.
“Neither myself nor the SNP will shy away from criticising Russian policy when we believe it is merited.”
Today, an SNP Spokesperson told Express.co.uk: “The First Minister stood up at a press conference literally the day after the Alex Salmond show was announced – three years ago – and made her views clear.
“This is little more than a smokescreen to try and conceal the devastating criticisms by the ISC report of the Tory government’s negligence in failing to even assess the level of Russian interference into the EU referendum.
“If Labour and the Tories really want to move things forward then perhaps they should be looking into unelected Labour and Tory Lords’ business links with Russia, which was one of the most serious conclusions from this report.”
Mr Salmond resigned his membership of the SNP in 2018 and has not yet expressed any intention to return to Scottish Politics.
The former leader of the party said he did so to avoid internal division within the party at the time.
Alex Salmond’s representatives have been approached for comment.