Two-thirds of Australian voters, including more than half of all Coalition supporters, believe claims that asylum seekers' hands were deliberately burnt by Australian border protection authorities should be investigated.

That is despite the Abbott government refusing to launch an investigation into the claims, while slamming media organisations such as the ABC as ''malicious'' for reporting them. The result comes from the latest Fairfax-Nielsen poll conducted among 1400 voters across the country from Thursday to Saturday last week.

The ABC has also been strongly supported in the survey, with just three in 10 voters viewing the publicly funded national broadcaster as politically biased while 59 per cent said it was not.

Asked if they thought allegations that the navy had deliberately burnt the hands of asylum seekers warranted an investigation, two thirds of respondents, or 66 per cent, answered yes.

Even among Liberal and Nationals voters, the proportion in favour of an investigation was safely in a majority at 55 per cent. Those satisfied with the claims being dismissed as hearsay constituted just 31 per cent.

Among ALP supporters, the ratio in favour of investigation was 75 per cent - a figure that jumped to 88 per cent among Greens voters.

The government launched an unprecedented attack on the ABC earlier this month for reporting that Indonesian police were investigating allegations that Australian navy personnel forced asylum seekers to hold on to burning hot engine pipes aboard their boat as a form of punishment. The initial story showed graphic photographs of burnt hands along with the suggestion that the injuries appeared to support the torture claims.

The ABC subsequently acknowledged that its report may have lent too much weight to the veracity of the torture allegations, but stood by the story from its Jakarta correspondent, George Roberts.

However its reportage became a focal point for a slew of conservative-led attacks alleging the ABC was left-leaning, culturally biased against the Coalition, and without mature judgment.

Prime Minister Tony Abbott complained the ABC too often took ''everyone's side but Australia's'', as he criticised it for lacking a basic affection for the home team. He said the ABC should have given the navy ''the benefit of the doubt''.

Defence Minister David Johnston, however, made those comments look mild, admitting he was so furious at ABC management that he had taken a week to cool down enough to speak publicly.

He attacked ABC management for using ''weasel words'' to justify its reporting, which he said had ''maliciously maligned'' the navy.

''If ever there was an event that justified a detailed inquiry, some reform and investigation of the ABC, this is it,'' he said.

While the Abbott government has railed against the ABC, 67 per cent of respondents said they believed it provided a more balanced presentation of news than commercial television news services. Just 15 per cent trusted commercial television news more.

Even among conservative voters, over half (53 per cent) said the ABC was the more balanced television provider.

Among the 31 per cent who felt the ABC was biased, a third called it ''pro-ALP'', 15 per cent said it was ''left-wing'', and another 7 per cent described it as ''anti-Coalition''.

However, just 1 per cent branded it either ''un-Australian'' or ''anti-Australian''.

Support for the ABC has softened slightly, however, with the 67 per cent backing of its news and current affairs services dropping 3 percentage points over 14 years, when its support was measured at 70 per cent.