Cory Bernardi believes his decision to quit the Liberal Party might strengthen government MPs' support for Malcolm Turnbull.
The outspoken senator, who has moved to the cross bench to form the Australian Conservatives, insists defecting was the toughest path he could have chosen, denying his decision will destabilise the prime minister's leadership.
"That's up to Liberal Party colleagues. It also could strengthen them around him," he told ABC radio on Wednesday.
Mr Turnbull said Senator Bernardi should resign from the upper house, especially because he's talked about the importance of keeping faith with the electorate.
Only seven months ago the people of South Australia elected him for a six-year term as a Liberal senator, he told reporters in Canberra.
"So the honourable thing for Cory to do is to resign for the Senate and run again at the next election as an independent."
Cabinet minister Christopher Pyne - previously a fierce factional rival of Senator Bernardi - emphatically backed calls for the renegade to resign and re-contest his seat as an independent.
"He would never have been elected if he wasn't on the party ticket," Mr Pyne told Adelaide radio station FiveAA.
"If Cory is so popular as he seems to think that he is, he would apparently easily get re-elected as an independent."
