LGBTIQ+ advocates want the state to ban the so-called therapy, with a recent Tasmania Law Reform Institute report making 16 recommendations for law changes to prevent the practice.
"I support acting on the recommendations of the law reform institute report," Mr Rockliff told an estimates hearing on Monday.
"The attorney and I are working together on these matters. I will be leading the change."
Victoria, Queensland and the ACT have banned conversion practices, which aim to change, suppress or eradicate someone's sexual orientation or gender identity.
Mr Rockliff said he had spoken with survivors of conversion practices and would seek to table legislation in parliament following community consultation.
"I understand how much it has affected individuals to the detriment of their wellbeing, to put it mildly," he said.
"It is clear to me as the minister for mental health and wellbeing that there needs to be change. I do take this very seriously."
Among changes, the law institute proposes amendments to stop unregistered and unqualified people from purporting to assess, diagnose or treat the sexual orientation of others.
It noted conversion practices can cause serious and lasting harm.
"We do suggest (conversion practices) be banned ... but (not that breaking the law) simply means you'll go to prison," report co-author Martin Clark said in May.
"What we're recommending is a much more nuanced set of statutory reforms."
Tasmania's Catholic Church has indicated it is deeply concerned about the recommendations, and is undertaking a detailed review of the report.
The law reform institute says the proposed changes would not impact expressions of faith, or philosophical or personal views about sexual orientation or gender identity.
State Greens leader Cassy O'Connor welcomed the premier's move, describing conversion practices as "homophobic, religious whackery dressed up as therapy".
Glen Worrell, who experienced more than two decades of conversion practices including one nine-hour prayer session with an exorcism, has said law change will save lives.
"The psychology always says 'you are flawed, you are sinful, you are broken and you need to be fixed'. It is a never-ending cycle of guilt and shame."
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