Speaking at a press conference, Porter began by addressing the parents of the woman involved in the accusations.
"The things that have been claimed to happen did not happen. I do not mean to impose anything more upon your grief.
"I hope that you will also understand that, because what is being alleged did not happen, I must say so publicly."
The allegations against Porter were circulated last week in an anonymous letter which was sent to police and political leaders including Australian Prime Minister Scott Morrison, former Prime Minister Malcolm Turnbull and Greens Senator Sarah Hanson-Young.
The woman who made the allegations claimed she met Porter when she represented South Australia on a state debating team when she was 16 and he was 17.
In an unsworn statement she claimed the alleged rape happened in 1988 after a night of drinking and dancing in Kings Cross.
"I did not sleep with the [alleged] victim. We didn't have anything of that nature happen between us," Porter said.
"I remember the person as an intelligent, bright, happy person."
He confirmed that he would not be standing down as Attorney-General, claiming if he was made to do so then there would be "rule of law left" in Australia.
"If I stand down from my position as Attorney-General because of an allegation about something that simply did not happen, then any person in Australia can lose their career, their job, their life's work based on nothing more than an accusation that appears in print," Porter said.
"If that happens, anyone in public life is able to be removed simply by the printing of an allegation. Every child we raise can have their lives destroyed by online reporting of accusations alone."
Porter said if he were step down it would set a bad precedence for people who find themselves in a similar situation.
"My guess is if I were to resign and that set a new standard there wouldn't be much need for an Attorney-General anyway because there would be in rule of law left to protect in this country.
"So I will not be part of letting that happen while I am Attorney-General and I am sure you will ask and I will state to you, I am not standing down or aside."
While Porter will not be resigning as Attorney-General, he will be taking a period of mental health leave.
"I am going to take a short period of leave to assess and hopefully improve my own mental health," he said.
"All of my life I have just pushed through, but for the many caring family and friends who have asked me that question over the course of the last week, 'Are you OK?' I have got to say my … answer is I really don't know. I am not ashamed to say that I am going to seek some professional assessment and assistance on answering that question over the next few weeks."
On Tuesday, NSW police confirmed they will not proceed with an investigation.
"NSW Police have since sought legal advice in relation to these matters,'' a spokesman said.
"Based on information provided to NSW Police, there is insufficient admissible evidence to proceed.
"As such, NSW Police Force has determined the matter is now closed."
Earlier this week, Mr Morrison revealed he had spoken to the minister at the centre of the claims, saying he "vigorously" denied the accusations.
When asked if he believed the denials, Mr Morrison said it was a matter for the police.
