"These are bizarre and absurd allegations by a disaffected, sacked employee," Dr Napthine told reporters on Thursday.
"They are not worth the paper they are written on."
Mr Napthine said he was advised the material was inappropriate but not illegal, and said Mr Coulson had been sacked for other matters not related to this.
"Mr Coulson is lashing out as a disaffected, sacked employee and he is making bizarre allegations," he said.
Mr Coulson, 59, was a former public servant who had worked with Mr Baillieu in opposition and was in charge of the government's Freedom of Information strategy before he was sacked, the newspaper said.
But Mr Coulson has told the Herald Sun and ABC radio he will vigorously defend the allegation that he accessed pornography on any government system.
Deputy Labor leader James Merlino described the allegations as shocking and needed to be investigated by police.
"This would be breaking every rule, every code of conduct, common sense, decency," Mr Merlino told Fairfax Radio.
"This needs to be referred and investigated immediately by Victoria Police and federal police in regards to allegations of illegal pornographic material.
"Denis Napthine can't sweep this under the carpet. He needs to make a full and frank explanation to the parliament today. What did he know? How long has he known it? Has he spoken to each and every cabinet minister around his table?"
- AAP