Speaking during a discussion about funding for the arts, Dean criticised the scribe for accepting a large sum of money to appear at the state's Stillwater library, branding him a "pencil-necked little weasel who stole $45,000 (£27,400) from the state of Minnesota".
However, the Republican has since expressed remorse for his comments while maintaining the underlying criticism.
"My mum is staying with us right now," he told Minnesota Public Radio. "My wife's out of town, and she was very angry this morning and always taught me to not be a name caller. And I shouldn't have done it, and I apologise."
Gaiman, who donated the remainder of his $45,000 to charity after settling agents' fees, responded to Dean's initial remarks via Twitter. "I don't like the idea that a politician is telling people that charging a market wage for their services is stealing," he wrote.
In addition to his work as an acclaimed comic writer, Gaiman is renowned for his fantasy prose novels. He recently scripted an episode of Doctor Who titled 'The Doctor's Wife', scheduled to air on May 14.
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