“You have to do something,” said Mr. Petraeus at the gala. (Here’s an edited transcript of his comments.)

An Isolationist’s nightmare? Mr. Petraeus generally enjoys doting support from the conservative circles around Australia’s Liberal government. And he was made an honorary officer of the Order of Australia — one of the country’s highest honors — in 2009, under a previous Labor administration. But as populist politicians have risen and become more alarmist about Islam, so too has he become more vocal about what he has described as “generational struggle” in the region.

Many of his recent public statements — including appearances on PBS and in The Wall Street Journal — have advocated for hawkishness in response to the threat of Islamist extremism.

The regional scholars we talked to Monday were divided on the approach he’s laying out.

Alan Dupont, a nonresident fellow at the Lowy Institute, agreed with Mr. Petraeus’s threat assessment. “We’ve been caught napping,” he said. “He’s absolutely right to awaken the Australian public consciousness about the seriousness of this. We’ve got to nip this in the bud quickly, otherwise Petraeus will be right in his predictions of a generational struggle in our own region.”

On Friday night, Mr. Petraeus also suggested that Australia is “not going to drone strike or Delta Force your way out of this problem. You’re going to have to have forces on the ground.”