This process can be arduous and complex, meaning those who want to change their sex have opted against embarking on the process.
A working group was formed last to figure out how to make this process easier and its report was released this morning.
Tinetti said a significant number of the report's recommendations will be adopted.
"This Government understands that self-identification is a significant issue for transgender, non-binary and intersex New Zealanders, and is committed to making it easier for people to formally acknowledge their identified gender."
The changes include funding a service that provides free face-to-face or over the phone advice to people at each step in the process, as well as rolling out guidelines on ensuring more "trans-inclusive and affirming language" at Family Courts.
The Government will also simplify the process of applying for a new birth certificate after a Family Court declaration has been granted.
These were some of the recommendations made by a working group tasked with reducing barriers to changing people's registered sex, which have been adopted by the Government.
Although the Government said it would implement, or work to implement, most of the 38 recommendations, there are some which won't be adopted.
The working group recommended that free legal representation be made available for people seeking to change the sex recorded on their birth certificate.
But the Government said that it already has systems in place which provide free legal aid, "if hardship circumstances apply".
Meanwhile, Tinetti said she continues to "urgently progress" the work needed for Cabinet to get the bill before the House.
"I will take a range of perspectives into account as I make decisions on the future of the Bill, including whether it will come before Select Committee again. It is important we get this right."
Births, Deaths, Marriages, and Relationships Registration Bill had passed its first reading during the last term of Parliament.
But the gender self-ID clause was added during the select committee process, prompting legal concerns, according to then minister Tracey Martin, who was in charge of the bill.