Victorian Premier Daniel Andrews has urged the Federal Government to abandon plans for a public poll on same-sex marriage.

Mr Andrews has written to Prime Minister Malcolm Turnbull urging him not to hold a plebiscite on legalising marriage for same-sex couples.

In the letter, Mr Andrews argued the plebiscite would legitimise hateful debate about LGBTIQ issues.

He said there was no public poll before the Marriage Act was changed to specify that marriage was a union between a man and a woman.

"In 2004 the law was changed to be fundamentally unequal, to be discriminatory, to be unfair, without a national plebiscite," Mr Andrews said.

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He said the $160 million plebiscite would be wasteful.

"But the cost is not best measured in numbers," Mr Andrews said.

"The cost is best measured in the pain, the anguish, the sense of inequality, the sense of not being treated fairly.

"This will be a harmful, spiteful debate — it will give legitimacy to hurtful views, views that are essentially bigoted."

The Premier said he did not want to speculate about what would happen if the plebiscite occurred, and returned a vote against legalising same-sex marriage.

But he would not say whether Victoria would go its own way in introducing marriage equality laws.

"I haven't ruled that out," Mr Andrews said.

"We have a proud history in this state of changing the law and trying to be the progressive capital of our nation and that's not going to change."

Last month, Mr Turnbull said he was confident Australians had the maturity to have a respectful discussion about the issue.

Support services report increased demand for counselling

Victoria's Gender and Sexuality commissioner Rowena Allen said the debate over the plebiscite was already hurting LGBTIQ people.

Premier Daniel Andrews, accompanied by his wife Catherine, led the Pride March in Melbourne last year. ( ABC News: Sarah Farnsworth )

She said calls to the gay and lesbian phone counselling switchboard had doubled in the past three months.

Family support agency Drummond Street Services has also reported a surge in demand for counselling services.

Ms Allen said it was difficult to say whether the possibility of the plebiscite was entirely to blame, but she was concerned about the mental health impacts of a public debate.

"The sort of things that I'm receiving from people, what they're experiencing are really horrific," Ms Allen said.

"Absolutely horrific. Language that we haven't heard for 10 years is back.

"We're already seeing the effects of talking about a plebiscite on the mental health of lesbian, gay, bisexual, transgender diverse and intersex Victorians. We need to put the debate down and just have equality."

Lack of recognition 'makes me want to cry'

Merryn Tinkler has been with her same-sex partner for 25 years, and they have a teenage son together.

She said she was upset by the lack of recognition for her family.

Merryn Tinkler, with her son Matthew, says she wants her family recognised. ( ABC News: Stephanie Anderson )

"It makes me want to cry that I can't be recognised, that I'm not equal," Ms Tinkler said.

"My son is 19. We've fought a long battle.

"Matthew was born into an environment where he wasn't recognised... we had to go through courts, family courts so that my partner could be recognised as a parent to our son."

She said, thankfully, the environment has changed.

"We need a government, a national government, to step up and actually acknowledge that change, acknowledge that change is real," Ms Tinkler said.

"There's nothing special about us.

"We're a normal family, nothing special or scary about us."