Williams, who was ordered by the Supreme Court to pay $35,000 in costs, said he did not want to comment.
The founder and executive director of lobby group NZ Taxpayers Union, Williams had accused Craig of defaming him at a press conference and in pamphlets which were posted to 1.6 million households around New Zealand.
The pamphlets were a response to Williams' allegation that Craig had sexually harassed his former press secretary Rachel MacGregor and had sent her unsolicited cards, letters, compliments and romantic poetry.
After the four-week High Court trial in 2016, the jury found in Williams' favour and awarded Williams the highest amount for defamation damages in New Zealand's legal history.
The judge, Sarah Katz, set aside the jury's verdict on the grounds that the damages were excessive and that she had misdirected the jury on one aspect of the case. She ordered a retrial on the both liability and the size of the award.
After Williams appealed, the Court of Appeal ordered a retrial only on the size of the award - and not on the jury's verdict on liability.
In the Supreme Court, Craig had sought a full retrial and Williams had sought a reinstatement of the jury's award of damages.
In a majority verdict from the Supreme Court, the judges said it could not be concluded that judge's misdirections did not result in a miscarriage of justice. For that reason, they ordered a new trial on both whether Craig defamed Williams and on the possible damaged to be paid.
The Court of Appeal said a more appropriate amount of damages would have been $260,000.