In some areas popular opinion is directly opposed to Government policy.
The poll found 61 per cent rejection of Labor's decision to allow sales of uranium to India - also a Coalition policy - and almost 80 per cent believe Australia's policy on Fiji is wrong.
The overwhelming majority want Canberra to reopen ministerial-level contacts between the two countries.
But Prime Minister Julia Gillard's intention to bring most Australian troops back from Afghanistan a year ahead of schedule has wide backing.
Opposition to involvement in the war has risen to 65 per cent, although most support a continuing, limited counter-terrorism role for special forces there.
Asia, meanwhile, looms large in Australian minds.
The poll said two-thirds believed it was very important for the nation to be viewed positively in the region, with more than 80 per cent supporting government-funded moves to improve relations through broadcasting or other programmes.
Respondents also advocated further involvement in Asian political forums, an increase in diplomatic representation, and a greater emphasis on learning Asian languages. But there is less support for increasing efforts to attract Asian migrants and investment, with wide opposition to the sale of farmland - a sensitive issue that has also spread to concern about the control of mineral resources by state-owned Chinese groups.
Australians are generally feeling better about China - the poll's "thermometer" of affection for the country has risen six points to 59 "degrees" - and recognise its importance to their economy.
A majority of 58 per cent also believe China is unlikely to become a military threat to Australia within the next 20 years.
But the poll found that 95 per cent believe China is or will become the region's dominant power - and, of these, more than half felt either "very" or "somewhat" uncomfortable with the development.
And Australians continue to turn to the US.
Support for the importance of the American alliance has risen to a Lowy poll record of 87 per cent, with three-quarters of respondents naming the United States as Australia's most important security partner in the coming decade.
Australians prefer Barack Obama as president over Republican Mitt Romney by a ratio of eight to one, and three-quarters supported his announcement last November of plans to base 2500 Marines in the Northern Territory.