On Saturday, in the wake of the shooting in Connecticut where 26 people were killed at an elementary school, Mr Turnbull replied to a tweet by Mr Murdoch.
‘‘Terrible news today. When will politicians find courage to ban automatic weapons? As in Oz after similar tragedy,’’ Mr Murdoch said.
Mr Turnbull then observed: ‘‘@rupertmurdoch I suspect they will find the courage when Fox News enthusiastically campaigns for it.’’
According to Twitter Counter, Mr Turnbull - who currently has about 136,000 Twitter followers - got an extra 1800 followers out of the comeback.