Dr Hewson believes the prime minister should call out his predecessor especially over energy policy, which Mr Abbott focused on during a speech in London this week.
"How long do you want to sit back and be beaten up, because that's what (Mr) Abbott's doing," he told Fairfax Media on Thursday.
Mr Turnbull should draw a line in the sand in adopting a progressive clean energy target, in the full knowledge that Mr Abbott would fight back, he said.
Dr Hewson thinks Mr Abbott would "make a bit of noise" and there would be "a few that would back him", but ultimately voters would appreciate the prime minister standing up for his beliefs.
"It's time for Malcolm to just take a stand and I think the electorate is looking for him to show leadership on so many issues," he said.
Asked whether he values or appreciates Mr Abbott's public interventions on climate policy, Treasurer Scott Morrison refused to comment.
"I make decisions in government. I don't commentate on my colleagues," he told ABC TV.
"Colleagues are free to say what they say."
Education Minister Simon Birmingham also batted away the question.
"I bet your viewers care more about their electricity bills than Tony Abbott," he told Nine.
