Australia wants Singapore to be part of its family, Tony Abbott says, agreeing to work more closely on the region’s defence and terror challenges.

The Prime Minister on Monday sealed a comprehensive strategic partnership with Prime Minister Lee Hsien Loong that Mr Abbott said should be more than just another diplomatic pact.

“My hope is that underneath the phrase will be a new intimacy between Australia and Singapore,” he told an audience of business leaders.

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“I don’t simply want Australia and Singapore to be friends, I want us to be family in the years and decades to come.”

In the agreement, both countries agreed to review the free trade agreement by July next year and review the Foreign Investment Review Board threshold for Singaporean investors.

A memorandum of understanding to co-operate on counter-terrorism was signed, and defence co-operation will be furthered with increased access to training areas and joint development of military training facilities in Australia.

Mr Lee said Australia and Singapore shared an interest in peaceful resolutions to regional tensions.

They could do more together on counter-terrorism, he added, suggesting they could learn from each other, particularly on de-radicalisation.

Mr Abbott on Sunday visited a religious rehabilitation group that was an example of how Singapore has helped jihadists and their families turn away from radical ideas.

“We’ve tried to guide the Muslim community in Singapore to not be misled by deviant and extreme and unsound interpretations of the faith to do very evil things like ISIS is doing,” he said.

Australia’s deepening engagement with Singapore comes as Indonesia’s former foreign minister Marty Natalegawa flagged a “key juncture” in relations between the immediate neighbours.

Australia’s asylum boat turnbacks are “incompatible” with good relations, Dr Natalegawa says, while Indonesia’s executions of Andrew Chan and Myuran Sukumaran in April drove Australia to recall its ambassador.

But Mr Abbott has a different view of Australia’s place in the region.

“Australia is a country with almost no critics but many friends,” he told the business breakfast.

Mr Abbott enjoyed a busy schedule in Singapore, on Sunday night attending a barbecue to mark 50 years of diplomatic relations.

-AAP