The forced turn-back of asylum seeker boats to Indonesia has overwhelming public support in Australia, bolstering Prime Minister Tony Abbott as he sits down on Wednesday with President Susilo Bambang Yudhoyono.

A new poll also finds almost two-thirds of Australians back spying operations in Indonesia, another flashpoint for Mr Abbott to navigate after last year's revelations that Australia bugged Mr Yudhoyono's telephone.

Yet in a surprise result, the public is just about as happy to treat America - or even New Zealand - as an intelligence target a finding apparently at odds with Australians' strong support for the ANZUS alliance.