Australia's upper house Senate on Wednesday passed a measure to legalise same-sex marriage, perhaps as soon as next week, after lawmakers dismissed a conservative push to allow religious objectors to refuse service to same-sex couples.

Australians overwhelmingly endorsed legalising same-sex marriage in a postal survey run by the national statistics agency and the bill easily passed the Senate by 43 votes to 12.

Australia will become the 26th nation to legalise same-sex marriage, a watershed for a country where some states held homosexual activity illegal until 1997.

Conservative lawmakers had pressed for broad protections for religious objectors, among them florists, bakers and musicians, to refuse service to same-sex couples.

But amendments for lay celebrants to refuse to solemnise same-sex marriages and permitting caterers opposed to the unions to refuse service at wedding receptions were either defeated or abandoned during two days of debate in the senate, where same-sex marriage supporters are in the majority.

"The Australian people voted to lessen discrimination, not to extend it and we, the senate, have respected that vote by rejecting amendments which sought to extend discrimination, or derail marriage equality," Labour Senator Penny Wong, who voted down all the amendments, told Parliament.

The bill moves to the lower house next week, where conservative lawmakers hope for a renewed push to add measures exempting objectors to same-sex marriage from existing laws against discrimination.

"I do not think we have made these changes in a way which advances rights fully," said centre-right National Party Senator Matt Canavan.

Prime Minister Malcolm Turnbull's Liberal-National coalition government and the main opposition Labor Party have said they wanted to pass the law through parliament by Dec. 7.

If the legislation passes as expected, Australia will become the 26th nation to legalise same-sex marriage, a watershed for a country where some states held homosexual activity illegal until 1997.

Meanwhile, Victoria on Wednesday became the first state in Australia to allow terminally ill patients to end their life as its legislature passed a euthanasia law that other states are expected to use as a template.

The legislation, to come into effect in June 2019, will make it legal for any resident of the southeastern state with a terminal illness and with less than six months to live to request a lethal dose of medication.

Sufferers of some conditions, such as motor neurone disease and multiple sclerosis, can request a lethal dose even if they have been given up to a year to live.

"The implementation of the bill ... will give people hope and compassion, and that a good death will in fact be possible for people who are currently enduring difficult, difficult ends of life," Victoria's Health Minister Jill Hennessy said outside the state legislature in Melbourne after the lower house approved a law that had already cleared the upper house.

Many countries have legalised euthanasia, including Canada, the Netherlands, Switzerland, and some states in the United States, although the Australian government opposes it.

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