The Gender Recognition Reform (Scotland) Bill was passed by MSPs in December before being blocked by the UK Government.
The legislation would have made it easier for transgender people to obtain a gender recognition certificate (GRC), but critics warned it could impact on the rights of women and girls.
Amendments tabled during the process that would have stopped those charged with sexual offences from obtaining a GRC, as well as protecting single sex space exemptions were rejected.
Speaking to the PA news agency on Saturday, Mr Sarwar insisted his party was still right to back the Bill, despite saying the government was wrong to block the amendments.
“I would hope that the SNP have learned over the past few weeks that they were wrong to reject the amendments around sex offenders, they were wrong to reject the amendments around those who were on trial and they were wrong to reject the amendments around protecting single sex spaces in particular circumstances and I hope they can reflect on that,” he said.
But when asked if his party was right to vote in favour of the Bill without the changes being made, he said: “I think we were right.
“We made clear that this wasn’t the form of Bill that we would have brought forward if we were in government, this was an SNP Bill not a Labour Bill – they’re the government, they bring forward legislation.
“We were right to get the amendments we did, we were right to get the safeguards in we did, I think we were right to support removing the inhumanities of the GRC process, but there is still work to do.”
Labour MSP Pam Duncan-Glancy proposed an amendment at stage two of the Bill which inserted a provision saying the legislation would not have any impact on the Equality Act.
Asked what he thinks the future of the Bill should be, Mr Sarwar said he wanted both the UK and Scottish governments to “knock their heads together” and work in good faith to come to a solution.
“Right now it feels like everyone has lost – I don’t think anyone in our trans community feels any more protected since the passing of the GRR Bill and I don’t think the women who had legitimate concerns feel reassured since the passing of the GRR Bill,” he said.
“So, therefore, a good faith approach, where we try and move forward to try and build consensus and find a way through (is needed).”
Mr Sarwar earlier suggested to journalists that the Section 35 order from the UK Government – which blocked the Bill from achieving Royal Assent – should be rescinded while the differences between the two governments on the legislation are resolved.
The Scottish Government has until mid-April to challenge the order in court, with ministers repeatedly saying they planned to defend the legislation “vigorously”.
Social Justice Secretary Shona Robison added: “We accepted many of Labour’s amendments and they supported the bill. However, I have made clear, I could not support any amendment which would have a serious risk of being outwith the Scottish Parliament’s legislative competence.
“The Gender Recognition Reform Bill simplifies the process by which a trans person can obtain a Gender Recognition Certificate, which many find intrusive, medicalised and bureaucratic.
“The Bill does not introduce any new rights for trans people – it is purely about improving the way trans people gain legal recognition, which has been a right in the UK for 18 years.
“Our support for trans rights does not conflict with or continued strong commitment to uphold the rights and protections that women and girls currently have under the 2010 Equality Act. This Bill makes no changes to that Act.”