Crossbench Senator David Leyonhjelm has announced he will push on with a second attempt to redefine marriage because he is ‘reasonably confident’ enough major party politicians will vote it through.

On Thursday, the Liberal Democrat said he would trigger a final debate on the legalisation of same-sex unions next week, clearing the way for a vote in the upper house at some time in the future.

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“We want to kick the debate along,” Senator Leyonhjelm told the media at Parliament House.

“I am reasonably confident that if it comes to a vote on this issue, there will be a majority … very much a majority in favour,” he said.

If the Senate agrees, the debate on whether the definition of marriage should be expanded from “a man and a woman” to “the union of two people” will be scheduled for 26 March.

Senator Leyonhjelm’s first attempt failed in November last year, but his proposal has already had a minor win this year.

On Wednesday, the Greens passed a non-binding motion in the Senate calling for a conscience vote on the issue.

Under current Liberal Party rules, backbenchers could vote freely for gay marriage, but cabinet ministers would be forced to resign if they supported the bill.

Senator Leyonhjelm said he supported marriage redefinition because he is a staunch supporter of personal freedom.