Australian Prime Minister Tony Abbott is to face a second challenge to his position this year.

Former Liberal Party leader and communications minister Malcolm Turnbull asked Mr Abbott to open the party's leadership to an internal vote as the two-year-old conservative coalition government struggles in opinion polls.

Unlike Mr Abbott, Mr Turnbull supports gay marriage, wants Australia to replace the British monarch with an Australian president as head of state and backs a policy of making polluters pay for their carbon gas emissions.

Mr Abbott announced the ballot of ruling Liberal Party politicians would be held in Parliament House late on Monday.

"This country needs strong and stable government and that means avoiding at all costs Labour's revolving-door prime ministership," Mr Abbott said.

"The prime ministership of this country is not a prize or a plaything to be demanded. It should be something which is earned by a vote of the Australian people."

Mr Turnbulll earlier said the government was doomed to defeat with Mr Abbott at the helm.

"Ultimately, the prime minister has not been capable of providing the economic leadership our nation needs," he said. "He has not been capable of providing the economic confidence that business needs."

Mr Turnbull might not be the only candidate. Foreign minister Julie Bishop, the Liberal Party deputy leader, is regarded as a possible contender as well as social services minister Scott Morrison.

Nick Economou, a Monash University political scientist, said: "I find it hard to believe that someone would move on the leadership unless they were absolutely confident of their numbers."

The government has trailed the opposition in a range of opinion polls since April last year.

Mr Abbott survived a leadership challenge from within his party in February that was prompted by those polls and what some say were questionable judgments. At the time, Mr Abbott asked his colleagues to give him six months to improve his government's popularity.

Mr Turnbull, a 60-year-old former lawyer and merchant banker known for his moderate views, has long been considered Mr Abbott's chief rival.

He was opposition leader for two years before he lost a party-room ballot by a single vote to Mr Abbott in 2009.

Opinion polls show Mr Turnbull is more popular than Mr Abbott, but many of those who prefer him vote for the centre-left Labour Party.