A majority of Australians believe the federal government has a responsibility to accept people seeking asylum, a new survey has found.

The survey, carried out by pollster Redbridge on behalf of asylum support agencies, found more than half of those polled supported granting asylum seekers work and study rights while they await the outcome of their protection visa applications.

The survey of 1,508 Australian voters carried out in January, found that while some people supported tough policies for those seeking asylum, many supported compassionate responses.

The survey found issues around refugees and asylum seekers as some of the least important to voters in the lead-up to the federal election, with the cost of living, healthcare and the economy rated the top three. Just one per cent considered refugee issues as their top election priority.

The polling showed 35 per cent strongly or somewhat supported government powers to pay other countries to take asylum seekers or non-citizens Australia wants to deport. About 32 per cent were strongly or somewhat against the measure, while 23 per cent felt neutral.

Forty-two per cent of people opposed deporting asylum seekers to their country of origin, regardless of the risk of persecution or violence, while a third supported it.

More than two-thirds supported allowing those denied a protection visa through the former Coalition government’s “fast-track” system, which Labor dismantled after being elected, a chance to re-lodge an application through the new system.

The survey showed voters felt strongly about punitive measures for those in immigration detention, with 50 per cent backing powers to conduct more invasive searches compared with 22 per cent opposed.

The survey showed voters with more conservative leanings, or who accessed right-leaning media, were more likely to agree with tougher measures, while left-leaning respondents were more likely to agree with extending rights such as study or work.

Redbridge director Kos Samaras said it would be unwise of politicians to politicise refugee and asylum issues for gain.

“People don’t want their government punishing marginalised people. This is a clear message to both major parties – voters are watching, and they expect a fair and humane approach to refugees,” he said.