The woman and Mr Porter, who is currently taking leave from his role as a federal cabinet minister, were teenagers when the alleged rape occurred in 1988.
Mr Porter firmly denied the allegations, and the woman withdrew her complaint the day before she took her own life last year.
It is police custom and practice to respect the wishes of victims, and therefore the police investigation could not continue, Mr Fuller said.
"That is not (just) for the attorney-general, that is for every matter," he said.
Regardless, Mr Fuller said without the alleged victim or a signed statement from her, proceeding was "just an impossibility".
But in a tabled response to a question taken on notice, Mr Fuller revealed NSW Police had not been sent the extensive document laying out the woman's claims before declaring it could not investigate.
A summary email - with no attachments - was instead provided by the AFP on February 25 he said.
Mr Fuller's answers also revealed the woman had provided police with a two-page account of her claims in March 2020, and a friend of the victim in July 2020 had provided police with another 88-page document authored by the alleged victim.
Police also spoke to the victim's sister in September last year.
NSW Police spoke to the alleged victim five times on the phone and corresponded six times via email. A face-to-face meeting was scheduled in Adelaide for March 16.
Mr.Fuller's tabled response came after the ex-boyfriend of the woman said he had "relevant discussions" with Mr Porter over a number of years.
James Hooke, who is now senior managing director with Macquarie Group, on Friday offered to appear before an independent inquiry.
"I have what I consider to be clear recollections of relevant discussions I had with her over the years from mid-1988 until her death.
"I also have what I consider to be clear recollections of relevant discussions I had with Christian Porter from April 1992 in Perth and through the mid-1990s."
Mr Porter has said he does not recall having discussed the alleged rape with anyone.
Mr Hooke said he made himself known to NSW police last year after the woman's death and understood why they were unable to interview him.
When told of the statement from Mr Hooke, Mr Fuller said police officers had previously spoken to him.
But the commissioner said he was "more than happy" to talk to the deputy commissioner to ensure "all information has been properly assessed".
Prime Minister Scott Morrison continues to insist there is no reason under the"rule of law" for Mr Porter to face any action, but Labor leader Anthony Albanese said the issue "requires some resolution".
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