Transgender law reform proposed by the Scottish Government would lower the age limit for applications from 18 to 16, remove the need for medical evidence and reduce the required time spent living in the new gender from two years to six months.
It aims to make it simpler for trans people to get a Gender Recognition Certificate to legally change their gender.
Shirley-Anne Somerville told STV's Scotland Tonight programme the Scottish Government is "determined" to change the law before the 2021 Holyrood election, adding she wants to build "maximum consensus" for the plans.
Arguing trans and women's rights are not "mutually exclusive", Ms Somerville said there has been "a lot of misunderstandings" alongside legitimate concerns about the proposed legislation.
The Gender Recognition Reform (Scotland) Bill would continue to require applicants to make a declaration they have lived in their intended gender for at least three months and intend it to be a permanent transition, as well as having a three-month period of reflection after applying for a Gender Recognition Certificate.
Concerns have been raised about potential abuses of the easier process - for example, men using it to access women's spaces - although making a false declaration to change gender would remain a criminal offence.
In the interview, which will be broadcast by STV on Thursday evening, Ms Somerville said: "I absolutely appreciate that women's rights are exceptionally important.
"They have been long-fought for and long-campaigned on and there is absolutely nothing I would do as a member of this government to jeopardise any of that.
"So that's why I really do make sure that I listen to the concerns that are out there on the issue because we not only want to protect what we have as women but we want to make sure our rights are extended."
Ms Somerville said she was confident the legislation could be passed before the Scottish Parliament elections next year.
The Scottish Government is currently running a consultation encouraging people and organisations to submit their views on the proposed changes by March 17.
She said: "We have women's rights and we have trans rights - I don't see those aspects as mutually exclusive.
"What we're talking about here isn't something that's new. These people are in our community, they're part of our community.
"But they talk to us very specifically about how the current system deeply impacts on them, about the state of their mental health and particularly the high suicide rates within the trans community because they can't be recognised for who they are."