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Mr Craig has asked Dr Norman for a public apology, claiming the statements were defamatory.
Mr Craig said he had taken the step of getting his lawyers to assess the claim and seek a retraction and apology because he believed the comments were inaccurate and were widely broadcast.
He said Dr Norman's comments did not reflect his views.
"So I find it quite an offensive statement to think I might think these things, and certainly to publicise that nationally has gone too far.''
A letter from Chapman Tripp "invites'' Dr Norman to issue a retraction of the statements.
"Neither the context of an election year nor the occasion of the Big Gay Out provide you with a licence to say anything you like about Mr Craig ... They are also defamatory as it harms [Craig's] reputation to say he holds such sexist, derogatory and offensive views ...''
Dr Norman is yet to make a public statement about the letter, but is expected to do so this afternoon.
Mr Craig said he was aware different rules applied to politicians under the Defamation Act and it was an election year, but said Mr Norman had couched his comments as statements of fact rather than opinion.
He said if Dr Norman refused to apologise, he would consider taking it further including going to court.
"Our assessment is that it does cross the line. We set that standard that says things politicians say need to be more accurate, or express an opinion. It's a reasonably polite request, I think, and all we've asked for is a retraction and an apology.''
Mr Craig is renowned for calling in his lawyers over comments made about him - satirist Ben Uffindel was a previous target after a blog post written about Mr Craig.
Mr Craig said he had so far sent about six letters relating to defamatory statements and about two complaints to the Broadcasting Standards Authority. He said he had received apologies for each of them.
In December, TVNZ was required by the Broadcasting Standards Authority to issue an on air apology for an item on Seven Sharp about him.