Murdo believes that the SNP's controversial Gender Recognition Reform (Scotland) Bill is "seriously flawed."
He highlighted how it has led to the resignation of SNP Minister, Ash Regan, and a rebellion by eight other SNP MSPs, a move unprecedented in 15 years of the SNP in government in Scotland.
Commenting, Murdo Fraser MSP said: "Whilst I believe everyone recognises that the process for individuals to legally change gender does need simplification, what is being proposed in this Bill presents real difficulties. If passed, this law will allow someone as young as 16 to be granted a gender recognition certificate and legally change their sex simply by claiming to have lived in their new sex for three months, without producing any medical evidence of gender dysphoria.
"The implications of this are far-reaching and campaigners have pointed out it affects measures to tackle discrimination against women, like equal pay protections. It may also open what are currently single sex spaces and services to individuals who are biologically male and may present a threat."
Murdo continued: "The Equality and Human Rights Commission, which exists to promote and uphold equality and human rights across the UK, has warned the Scottish Government to pause this legislation, because of the unintended consequences. Regrettably, these calls have been ignored by the SNP Government, who are pushing on regardless.
"This is an area of public policy that we do need to take time to consider carefully and rushing through legislation as we have seen in the context of the Gender Recognition Reform Bill is simply not the way to approach these issues."
The Bill recently passed Stage 1.