On Wednesday, Mr Dutton said he agreed with the prime minister’s comments but conceded he had “canvassed different options around the composition of the program”.
He said any immigration minister would float different options for changing Australia’s intake.
Foreign Minister Julie Bishop said “no such proposal” was ever formally taken to cabinet, nor the government’s national security committee.
“It was never discussed with me,” Ms Bishop told reporters.
Australia’s rate of permanent migration has been capped at 190,000 since 2011 - back before Tony Abbott was prime minister.
Nearly every year the cap is met, but in the most recent 2016-17 financial year, the intake dipped to 183,000. The government has no obligation to fill the quota.
Mr Dutton said the final statistics for the 2017-18 year would be available in coming months and suggested the number would again be “less than 190,000”.
The 190,000 places cover permanent visas for workers, families and a smaller portion of permanent places for refugees.
But the figure does not tell the whole story of Australian immigration.
The country’s “net overseas migration” statistics, known as the NOM, track the flows of people in and out of the country.
It includes those who enter the country on temporary visas, including temporary working, student and tourist visas. It also includes Australians who leave the country, or return home after time overseas.
The Home Affairs department estimates 511,900 people will have arrived in Australia by the end of this financial year in June 2018.
Minus the 286,200 people who leave, and Australia should be left with a “net” migration of 225,700.