Prime Minister Malcolm Turnbull has doubled down on his character assassination of Opposition Leader Bill Shorten, labelling him a "fake" who "doesn't have a fair dinkum bone in him".

It follows an extraordinary tirade in Parliament on Wednesday in which Mr Turnbull attacked his counterpart as "a social-climbing sycophant" and a "parasite" who cosied up to billionaires.

Mr Shorten has in the past week taken to calling the Prime Minister "Mr Harbourside Mansion", a reference to his lavish Point Piper home and a term coined by Tony Abbott's former chief-of-staff Peta Credlin.

"Shorten is complete hypocrite," Mr Turnbull said at a press conference on Thursday. "He wants to play the politics of envy and yet he's been a sycophant to the billionaires of Melbourne for years and years - everyone knows that."