Anas Sarwar has been urged to give Scottish Labour MSPs a free vote on legislation which would make it easier for people to legally change their recognised gender.
It comes after the Gender Recognition Reform (Scotland) Bill passed its first parliamentary hurdle last month.
MSPs voted to approve the Bill at stage one by a margin of 88 to 33, with four abstentions.
The legislation, being brought forward by the Scottish Government, would simplify the process by which a person can obtain a gender recognition certificate.
It would reduce the length of time an applicant must live in their acquired gender from two years to three months, with an additional three-month reflection period.
The minimum age for applying for a certificate would also be reduced from 18 to 16 under the legislation.
First Minister Nicola Sturgeon has insisted on the importance of protecting and enhancing the rights of trans people.
In making the case for the Bill, the SNP leader has also argued that the rights of women and the rights of trans people do not need to be in conflict.
However, the legislation has proved controversial and has been met with fierce opposition, including from author JK Rowling who has been an outspoken critic of the reforms.
Opponents of the Bill have argued that it could risk the safety of vulnerable women and have insisted on the need of protecting spaces for women.
SNP MSP Ash Regan resigned as a minister ahead of a debate on the Bill in October, indicating that she could not vote with the Scottish Government.
Last week, it was reported that female members of Scottish Labour have “grave” concerns about the Bill.
A leaked report by the party’s Women’s Committee claimed that 45% of respondents did not agree with the proposals.
It is despite Scottish Labour MSPs voting for the Bill at the Scottish Parliament.
There are now calls for the party’s leader, Anas Sarwar, to allow Scottish Labour MSPs to vote freely on the legislation.
Scottish Conservative MSP Tess White has written to Sarwar urging him to enable his party’s MSPs to do so.
In the letter, White pointed to previous scepticism over the legislation outlined by Scottish Labour MSPs, and suggested that a party whip will “only help” Nicola Sturgeon.
Scottish Labour and the Scottish Government have been contacted by STV News for comment.
“Women, girls and campaigners across Scotland have been dismayed to see Labour fall meekly in behind the SNP over these misguided reforms,” said White.
“Concerns over this Bill cut across party divisions and Labour members have expressed their doubts in the past – so it has been deeply disappointing to see Anas Sarwar try to silence the valid opposition of MSPs within his own ranks.
“We all agree on the need to improve trans rights, but it’s clear we must also protect vulnerable young people and the hard-won rights of women and girls.
“Sadly, Labour seem determined to ignore the legitimate fears of the EHRC, the UN Special Rapporteur on violence against women and girls, and even members of their own party.”
White called on Scottish Labour MSPs to “vote with their consciences” on the issue.
She continued: “Labour’s party whips are playing right into Nicola Sturgeon’s hands and in the process, letting down women, girls and vulnerable people all across the country.
“I urge Anas Sarwar to follow the Scottish Conservatives’ lead and allow his MSPs a free vote to express their legitimate opposition.
“If he won’t, then I hope Labour MSPs will choose to vote with their consciences and stand up for women and girls rather than toe the party line.”