Turnbull government minister Peter Dutton has launched a fresh assault on Fairfax Media, saying the public didn't miss the company's "left-leaning" journalists when they went on strike to protest looming job losses.

But Fairfax Media chief executive officer Greg Hywood quickly hit back, saying in a statement: "Once again Peter Dutton shows why no one rates him."

Appearing on Fairfax-owned Sydney radio station 2GB on Thursday, the Immigration Minister was asked by shock jock Ray Hadley whether he was concerned writers at The Sydney Morning Herald and The Age appeared to be praising the Turnbull government's second budget.

Mr Dutton, a regular public critic of media organisations he feels are hostile, used the question to launch another attack on the media company.