Liberal Democrats’ senator David Leyonhjelm has threatened to trade his vote on temporary protection visas or other legislation to force the Liberals to allow a conscience vote on gay marriage.

In the latest headache for Prime Minister Tony Abbott, Leyonhjelm said he was “not going to be fobbed off” on the matter.

His bill would seek to “deregulate marriage”. He said “the time is right” to bring forward the change, arguing that as a conservative, straight, middle-aged senator whose vote was important to the government he was in a good position to do so.

He was hoping to get a conscience vote by persuasion but was willing to use leverage if necessary.

The government’s legislation to re-introduce TPVs was defeated in the old Senate. Leyonhjelm said “the government will seek my support. I don’t care either way whether they go through or not. It’s neither here nor there to me.”

Labor allows a conscience vote on gay marriage; Abbott has previously said it would be up to his party room as to whether MPs would be able to vote as they liked. Abbott had hoped the question of gay marriage wouldn’t come before the parliament this term.

Leyonhjelm said that during his brief time in parliament he had met many people from the major parties who had confided that they broadly agreed with classical liberal or libertarian principles that governments should leave people alone, “including staying out of our private lives”.

The Liberal Democrats argued gay marriage is a matter for individuals to decide, not the government.

“For those of you who have a problem with homosexuality for some reason or another, we’re not asking for your approval.

"I ask merely for your tolerance. If your private life is nobody else’s business, I ask you to understand that the private life of others is none of your business, and it is simply not your role to impose your views on others,” he said.

“To those who support these principles but are not going to support us, I ask, well, what are you doing here?

"It is not the job of governments to define relationships. In fact the day will come when we look back on the role of governments to grant marriage certificates based on gender as the bizarre misappropriation of power that it is.”