At a press conference and in a pamphlet sent to more than 1.6 million households across the country, Craig called Williams a liar and vowed to take action against him.
Williams then filed defamation proceedings in the High Court, saying he did not lie about Craig.
The trial started on Monday before Justice Sarah Katz and a jury in the High Court at Auckland. It will run for about five weeks.
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So far the jury has heard lengthy evidence from Williams and from former Conservative Party chief executive Christine Rankin.
Today Craig's lawyer Stephen Mills QC is cross-examining Williams.
Just before the lunch break Mills told the court he intended showing the jury correspondence and text messages MacGregor sent to Craig during her time as his press secretary.
He has not yet indicated the nature of the material.
MacGregor is set to give evidence tomorrow.
The jury will also hear from Craig.