Scottish Green MSPs will walk away from the Bute House Agreement unless the next first minister challenges the UK Government's decision to block Holyrood's gender law reforms.
In a statement, the party said that not doing so would "set a very damaging precedent and would be incompatible with any belief in Scotland's right to self-government."
The threat from the Greens came after Kate Forbes said she would be "loath" to go to court over the Section 35 order.
READ MORE: Greens may exit SNP deal if Kate Forbes becomes FM prompting election
The Gender Recognition Reform Bill - passed by Holyrood in December - simplifies the process for obtaining a gender recognition certificate by removing the need for a medical diagnosis of gender dysphoria, sometimes described as self-id.
It also reduces the length of time someone would need to live in their acquired gender from two years to less than 12 months, and lowers the minimum age for applications from 18 to 16.
Last month, for the first time in the history of devolution, Scottish Secretary Alister Jack made an order under section 35 of the Scotland Act to stop the legislation from receiving royal assent.
He said the Bill would impact the UK-wide Equality Act.
Nicola Sturgeon has disputed that and promised to challenge the Tory minister's veto in the courts.
READ MORE: Nicola Sturgeon confident SNP members will pick 'someone of ability' to replace her
Ms Forbes told STV she would not continue with that course of action: "Well, I don't think that we should challenge the Section 35 in court, because I think the public want us to focus on things like the NHS, on making the case for independence, on the cost of living crisis, not on another court challenge, but I would engage with the UK Government to look at how we amend the Bill further."
Her main rival in the contest, Humza Yousaf said he would continue the legal challenge.
“This is about an assault, an attack on our very democratic institutions and yes, I think we should absolutely be challenging that in court," he said at his campaign launch in Clydebank.
“Somebody's really going to suggest to me that the first time a Section 35 order is going to be used by the UK government that we lay down and allow them to trample over the will of the Scottish Parliament on a bill that was not just supported by the majority, but had support from every single political party in that chamber?”
READ MORE: Humza Yousaf ditches Nicola Sturgeon's de facto referendum plan
A Scottish Green spokesperson said: “Eighteen months ago the Scottish Greens agreed to join the Scottish Government under the terms of the Bute House Agreement.
"It is a positive and progressive deal that was scrutinised and overwhelmingly endorsed by the membership and politicians of both parties, along with the full Cabinet.
“We are committed to working in cooperation with the SNP to ensure that it is delivered in full on behalf of the people of Scotland, including the Gender Recognition Reform Bill.
“The UK Government's decision to veto this clearly devolved Bill is an abuse of their power. As long term allies of the trans community, the Scottish Greens agree with the First Minister that this decision must be challenged robustly.
“Not to do so would set a very damaging precedent and would be incompatible with any belief in Scotland's right to self-government."
The Bute House Agreement saw the Scottish Greens co leaders Patrick Harvie and Lorna Slater become government ministers and share power with the SNP at Holyrood for the first time.
In return, the seven Scottish Greens MSPs are required to vote with the SNP on agreed policy areas as well to support the government in confidence and budget votes.
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