Australia's plan to permanently ban asylum seekers who arrive by boat from ever entering the country was in jeopardy on Tuesday when the opposition Labor said it would not support the ban.

Under the plan asylum seekers who are deemed genuine refugees and resettled in a third country would be permanently denied access to all Australian visas, including tourist and business.

"The idea that a citizen of the United States or Canada or New Zealand faces a life-time ban preventing them from visiting Australia in 30 or 40 years time is simply unacceptable to me and my Labor colleagues," said Labor leader Bill Shorten.

Conservative Prime Minister Malcolm Turnbull does not control the upper house Senate and without Labor support faces the complicated scenario of gaining the backing of eight of the 10 crossbenchers to legislate the ban.

Turnbull, whose popularity has hit a 14-month low, is struggling to implement policies without control of the Senate.

On Monday the Senate rejected a government plan to hold a national vote on whether to allow same-sex marriage, with opponents warning a public vote would be divisive, preferring a parliamentary vote to decide the issue.

Same-sex marriage is supported by 61 percent of Australians, a Gallup poll in August found.

Under Australia's tough border security laws, asylum seekers intercepted trying to reach the country by boat are sent for processing at detention camps on Papua New Guinea's Manus island and the tiny South Pacific island nation of Nauru.

Some 1,200 people are currently held in the camps.

The legality of forever barring people from entering Australia after they have been resettled in a third country, having been officially recognized as refugees, has been questioned by rights lawyers and refugee support groups.

The United Nations has said the plan would probably breach the Refugee Convention.