Dyson Heydon's decision to agree to speak at a future Liberal party event is further proof of why he should stand down as head of the royal commission into trade unions, Labor says.

Mr Heydon has faced sustained calls to step aside after Fairfax Media revealed that he had agreed to speak at a Liberal party fundraiser.

Royal commissioner Dyson Heydon: could rule on recusing himself as early as Friday. Credit:Andrew Meares

Mr Heydon is resisting demands he stand aside and is also refusing to answer questions about whether he will release all his correspondence with the NSW Liberals, relating to the event, as Labor is demanding.

Two emails Mr Heydon has published show he took nearly 24 hours to cancel his planned lecture after being told it was a Liberal party event.