Malcolm Turnbull garnered 61.9% of support compared to his rival Bill Shorten's 38.1%.

AFP/Sydney

New Australian Prime Minister Malcolm Turnbull has boosted his Liberal Party's standing in the opinion polls just days after ousting Tony Abbott, as he pledged to continue his predecessor's gay marriage policy.

A ReachTEL poll of 3,278 Australians - the first full survey since Turnbull assumed the top political job in a party coup on Monday night - showed support for the conservative Liberals against the Labor opposition surged by three percentage points to a 50-50 dead-heat.

Opinion polls play a key role in Australian politics and Abbott's poor showing over the past year, in contrast to Turnbull's popularity among voters, helped to undermine his leadership.

Turnbull, a 60-year-old multimillionaire former banker and businessman, also polled well against Labor leader Bill Shorten, garnering 61.9% of support compared to his rival's 38.1% in a question about who would make the better prime minister.

Abbott lagged behind Shorten 42.1% to 57.9% on a similar question put to voters in late August.

At the same time, the survey - conducted on Tuesday night and published by Channel Seven on Wednesday night - recorded an increase in support for the Liberals in a key Western Australian seat holding a by-election on Saturday.

Although the Liberals were expected to retain the seat vacated after the death of local member Don Randall, surveys previously indicated a swing away from the conservative party of 10%, amid the Abbott government's unpopularity.

Liberal concern about a second by-election in Abbott's Sydney seat of Warringah has lifted with the former leader saying he intends to stay in parliament.

"It's been a tumultuous week and I now intend to spend some time with my family to think about the future," Abbott told News Corp website news.com.au.

"But my intention is to remain in the parliament."

The latest polls came as Turnbull promised to stick with Abbott's plan to hold a referendum on same-sex marriage after the next election despite a new parliamentary committee report recommending a vote on the issue be held in parliament.

"Our policy is to have it (the referendum) after the next federal election," Turnbull, who is well-known for his support for gay marriage, told the Australian Broadcasting Corp late on Wednesday.

"Any policy can be changed but it would have to be considered by the cabinet and then obviously the party room (a meeting of lawmakers)," he added when pressed about whether any changes to the policy were possible.

Independent senator Glenn Lazarus, chair of the Senate committee, which has a majority of Labor members, warned a plebiscite could attract "very nasty and very aggressive advertising campaigns".

Same-sex couples can enter into civil unions or register their relationships in most Australian states, but the government does not consider them married under national law.