“I’m totally disgusted that the minister has used his powers to intervene in those cases,” said Jason Scanes, 41, a former army captain who has campaigned unsuccessfully for years to get a visa for his Afghan interpreter. “I’m just asking for a fair process and a fair go.”

Australia has always struggled with who belongs. The first British settlers slaughtered the indigenous population, and xenophobia has shaped the nation since its earliest days when the government restricted migration to whites. In some ways, Mr. Dutton, 47, a former police officer who has been in Parliament since 2001, is simply the latest in a long line of Australian leaders to seize on concerns about foreigners and security to advance their political careers.

But since taking over the immigration portfolio in 2014, he has also made the job uniquely his own.

Promoted last year to oversee even more of the country’s security apparatus as minister for home affairs, Mr. Dutton has become the country’s unsmiling face of enforcement, defending Australia’s harsh offshore detention camps, delaying citizenship applications, and arguing for cuts in overall immigration.

The approach has won accolades from conservatives at home and abroad, including President Trump. Just two weeks ago, Mr. Dutton also nearly became prime minister, leading a party coup, only to be defeated by Scott Morrison, another former immigration minister known for strict enforcement.