The first openly gay member of the federal Coalition says it’s “embarrassing” the Liberal Party has denied politicians a conscience vote on gay marriage.

Western Australia Senator Dean Smith’s call for a conscience vote comes as gay rights activists celebrate the New Zealand Parliament’s decision to legalise gay marriage last night. The NZ gay marriage bill — which was decided by a conscience vote — passed by 77 votes to 44, supported by Conservative Prime Minister John Key.

Smith, who entered the Senate in May last year, does not support extending marriage rights to gay and lesbian couples. He says changing the definition of marriage would break with tradition while making little practical difference to people’s lives. But he’s unhappy that Labor — traditionally the party of caucus solidarity — has allowed their MPs a free vote on the issue while the Coalition has not.

“As someone who adheres to the principles of the Liberal Party, I absolutely support a conscience vote,” Smith told Crikey. “It is a little embarrassing the ALP has stolen one of our virtues on this issue. I do not support gay marriage but I absolutely support a conscience vote.”

Coalition frontbenchers Malcolm Turnbull and Barnaby Joyce have previously backed a conscience vote, as has Liberal MP Simon Birmingham. Joe Hockey, George Brandis, Christopher Pyne and Greg Hunt have also reportedly argued for it internally. The Young Liberals backed a conscience vote in February.

Gay marriage campaigners have long believed convincing Tony Abbott to accept a conscience vote on the issue will be the key to legislative success. But even if a free vote was allowed, Smith believes legislation still wouldn’t pass the lower house on current numbers. Other Coalition sources say it would be extremely tight and a bill could squeak through.

Smith says a vote on civil unions would pick up votes from those with fixed views on marriage. “I’m very comfortable with civil unions,” he said.

In March Liberal MP Kelly O’Dwyer told Parliament she is “comfortable with the idea of same-s-x marriage” and predicted the Coalition would eventually “evolve” to support it. Crikey reported in February that Liberal candidates for the seats of Sydney and Melbourne Ports, Kevin Ekendahl and Sean O’Connor, both support marriage quality and a conscience vote. Melbourne’s Liberal Lord Mayor Robert Doyle has also backed the cause.