Humza Yousaf is under new pressure to pull out of power sharing agreement with the Greens after another long serving SNP MSP urged him to do so.
Christine Grahame indicated she had her concerns over the Bute House Agreement for some time as she called for the First Minister to reconsider his commitment to it.
"I think it's run its course," Ms Grahame told ITV Border this afternoon speaking from Holyrood.
"I've been here when we had a minority government and I think there is such a divergence of what the Greens and the SNP are looking for.
READ MORE: Why are the Scottish Greens considering leaving government?
READ MORE: Bute House Agreement: Greens to hold party exit vote
"I think the divergence is too great now and it's in the interest of neither party to continue. I would be content if the SNP were to say we are going to work as a minority government."
Asked whether she wanted the First Minister to exit the BHA, she replied: "Whoever does it, I would prefer it to be us."
Ms Grahame is the latest senior SNP MSP to back her party withdrawing from the deal with the Scottish Greens.
SNP MSP Fergus Ewing is a long standing critic of the arrangement, telling The Herald earlier this month he wanted his party out of the pact before the general election.
Former finance secretary Kate Forbes has also said the deal should be reviewed.
Earlier this week SNP MP Joanna Cherry said party members should have a new vote on the deal, while former health secretary Alex Neil said the two parties should '"go their separate ways."
SNP critics of the pact blame it for a fall in their party's support in the polls pointing to policies which became controversial such as the stalled deposit return scheme and new restrictions on fishing under plans to create highly protected marine areas off Scottish coasts.
Meanwhile, members of the Scottish Greens are to vote on whether to continue with the BHA at an extraordinary general meeting of the party next month.
More than 100 angry activists demanded the EGM last week after the Scottish Government dropped its landmark climate change target of reducing carbon emissions by 75% by 2030.
Scottish Greens co-leader Patrick Harvie wants the party to remain in government arguing that doing so is the best way of addressing climate change and delivering on other causes championed by the party on housing and in the area of equalities.
Mr Harvie has said he would step down from the party leadership if members vote to withdraw from the Scottish Government.
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