"We should bend that curve back upwards," he said in a written copy of Thursday night's speech.
"Let me say that I accept that our country is right to take measures to prevent illegal immigration.
"But now that our borders are secure I believe we can afford to be ambitious on immigration and generous towards refugees who come through the established processes."
Sir Frank acknowledged, however, that his way of thinking was now in the minority.
A poll commissioned by the Lowy Institute - the Sydney-based think his family founded in 2003 - suggests 54 per cent of Australians believe the immigration intake is too high.
The annual Lowy Lecture has been delivered in recent years by German Chancellor Angela Merkel, former CIA director David Petraeus and News Corp chairman Rupert Murdoch.
Sir Frank on Thursday spoke of his own history as a migrant coming to Australia in 1952 and how he felt the country regarded him as a future citizen from the very start.
"The challenge now is to give new arrivals that same sense of a personal stake in this country," he said.
"Of course, new arrivals should be grateful but we don't need their gratitude. We need their hard work and their belief."
The 87-year-old also urged Canberra to be more assertive with Beijing.
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The man who led Westfield for half a century explained he was no expert on the communist nation but "had some experience in negotiations".
"My experience tells me that if you don't look after your own interests, the person across the table certainly won't," he said.
"Our interests lie in having a balanced region - with the United States actively engaged - in which Australia and other countries are able to make their own independent decisions.
"And we should be clear with Beijing about that."