The Conservatives leader said in a statement today that Dr Norman's comments demonstrated a cavalier and reckless disregard for the truth.
Mr Craig planned to split the defamation claim into two stages "in the hope of fast-tracking a court hearing".
He hoped to get a declaration before the general election.
Dr Norman's lawyer Steven Price told Mr Craig's legal team last week that if a case went ahead, he planned to seek all of Mr Craig's correspondence which related to homosexuality, including personal emails.
Mr Craig said today: "Given the extensive debate around the redefinition of marriage, this is many hundreds, if not thousands of documents, and would result in prohibitive costs and time delays."
Mr Craig was one of the most high-profile opponents of a law change to legalise gay marriage last year.
Dr Norman said it appeared that Mr Craig had something to hide.
"One can only speculate what might be in Mr Craig's emails that he doesn't want them to come out in court about his views about gay New Zealanders."
He criticised the decision to make separate claims.
"It was a statement made in context, in one sentence. Mr Craig can't go and pick and choose which words he doesn't like."
Dr Norman said that it was likely he would contribute some of his own money to his legal defence.
He said that the legal challenge was a distraction in an election year but defending free speech was an important principle.
The party has been advised that defending the case was likely to cost around $70,000.
It will launch a campaign today to raise money for Dr Norman's legal fees.
Prime Minister John Key indicated he believed Mr Craig needed to harden up.
"If Mr Craig is going to be part of the Parliamentary process to be honest he's going to have to get used to a lot more rough and tumble than he's currently demonstrating.
"We all learn to develop a thicker skin as we spend our time here. The reality is this is the nature of Parliament."
Mr Key repeated his advice last week to his potential minor party allies including Mr Craig and Act Leader Jamie Whyte: "In the end, I think New Zealanders are interested in the issues that matter.
"People get up in the morning concerned about their jobs, their children, their health, their families, the communities they live in not whether Elvis is still alive, man walked on the moon or whether Russel Norman might have a view about what Colin Craig things about certain issues."