The call by the Scottish Conservatives comes after the First Minister revealed she had not raised the issue of signing up to the International Holocaust Remembrance Alliance (IHRA) definition of antisemitism with her new junior ministers, Patrick Harvie and Lorna Slater.
Former Scots Tory leader Jackson Carlaw had previously written to Ms Sturgeon after Jewish groups expressed their concerns that the Scottish Green Party refuses to endorse the IHRA definition of anti-semitism and had also voted in favour of a motion describing Israel as a “racist state“ based on “Jewish supremacy” and calling Zionism a “racist endeavour”.
Scotland’s Jewish organisations had also written directly to the First Minister raising their worries about the SNP government entering into a co-operation deal with the Greens.
However, it emerged on Friday that while aware of their concerns, Ms Sturgeon had not discussed the issue with either Mr Harvie or Ms Slater.
Scottish Conservative MSP for Eastwood, Jackson Carlaw, said: “If the Green party won’t sign up to a globally recognised position on anti-semitism, backed by every other party in Scotland, they’re not fit to serve in the Scottish Government.
“The Greens, especially their government ministers, must endorse this mainstream position or be removed from office. Their views are beyond radical. They are downright dangerous.
“Nicola Sturgeon cannot turn a blind eye to this extreme view held by her new coalition partners.”
He added: “It’s of real concern that she hasn’t even bothered to discuss this issue with the Greens, despite Jewish groups and the Scottish Conservatives putting it to the First Minister directly.
“Anti-semitism is still rife and we all must send a clear message that it’s wrong, especially those in positions of power.
“Scotland’s Jewish communities will be aghast if Nicola Sturgeon is willing to tolerate such extreme views in her government. She must act immediately.”
When asked about the Greens position on the IHRA Ms Sturgeon had said: ”I would hope everyone would sign up to the definition.
“The Scottish Government’s position on anti-semitism is clear and that’s the one all ministers are expected to sign up to and agree to.”
Asked if the Scottish Greens could continue in her government if they don’t accept the IHRA definition she said: “They are in my government.”
However Sammy Stein, chair of Glasgow Friends of Israel, said it was “very concerning” that there were now ministers with “such extremist views toward the state of Israel and Zionism.”
He added: "It would be important to know how long the FM will give the two Greens to adopt and agree to the Scottish Government's position on the definition of antisemitism.”
A spokesperson for the Scottish Greens said: “The Scottish Green Party abhors anti-semitism. There is absolutely no place for any anti-Jewish prejudice in society.”
A Scottish Government spokesperson said: “As the First Minister made clear, anti-semitism is utterly unacceptable and there is no place for it in Scotland.”