By Matt Siegel
CANBERRA (Reuters) - Australian Prime Minister Malcolm Turnbull came under pressure over same-sex marriage and from within his own party on Wednesday as parliament returned for the first time since a poor showing by his coalition government in elections last month.
Turnbull's Liberal-National coalition was reduced to a razor-thin one-vote majority in the lower house after an early poll to break a deadlock in the upper house Senate backfired.
The centre-left opposition Labor Party immediately dug in its heels over the government's proposal to hold a national plebiscite on same-sex marriage, which it considers expensive and unnecessary.
Labor, which wants a vote on the issue in parliament, has garnered enough support to block the plebiscite.
"We would not be true to ourselves if we said 'we think this is a terrible idea but, all right, have a plebiscite'," Labor Party Shadow Treasurer Chris Bowen told Sky News.
"We can recognize marriage equality, that's our job."
But while Labor's push for a vote on gay marriage was expected, less so was an embarrassing public rift with right-wingers within Turnbull's Liberal Party, who want to alter the country's race hatred laws.
Liberal Senator Bernardi, who is leading the push, has secured support from every backbench coalition senator save one to tone down the wording of the Racial Discrimination Act, according to a letter circulated by his office.
Some on the right argue that the current language barring speech that "insults" or "offends" is too vague and prioritizes political correctness over freedom of speech.
"The government is entitled to set its own priorities but as am I, for my own constituency, and that's the Australian conservatives who want to see reform in this space," Bernardi told the Australian Broadcasting Corp late on Tuesday.
"Now, I'm saying it's on the agenda."
The conservatives' push has exposed deep divisions within the government, which have been festering since the progressive Turnbull ousted conservative prime minister Tony Abbott in a 2014 party coup.
Under pressure from what Labor called in a press release "open revolt", Turnbull showed no signs of backing down.
"We have other more pressing, much more pressing priorities to address," he told reporters.
(Editing by Nick Macfie)