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The senior Morrison government figure outed himself as the accused man on Wednesday after sexual assault allegations against an unnamed minister surfaced last week.
Mr Porter will go on a short period of leave after speaking with his doctor about his mental health.
The woman, who was 16 at the time of the alleged rape in 1988, went to police last year but withdrew the complaint before taking her own life in June.
Mr Porter said he categorically denied the incident happened before declaring he would not stand down.
"Nothing in the allegations that have been printed ever happened," he told reporters in Perth.
The attorney-general said the woman's parents did not deserve the "frenzied politicisation" over the past few days.
Mr Porter said he stayed silent to respect the legal processes and rules since first hearing of a "whispering campaign" against him.
"All of this has happened and I have never been contacted in any substantive form by anyone putting to me the details of what appears is now being alleged against me," he said.
He said if he was to resign there would be no need for an attorney-general because there would be "no rule of law left to protect in this country".
Prime Minister Scott Morrison told reporters earlier this week the minister - who he did not name at the time - had "vigorously and completely denied the allegations".
There have been calls for an independent inquiry into the matter after NSW Police closed its investigation citing a lack of admissible evidence.
In an unrelated case, a former Liberal Party staffer has been accused of sexual assault by a fourth woman as questions mount over the Morrison government's handling of the first rape allegation.