The woman who received the message, who was 19 at the time, told Dagbladet on Friday that she did not consider the content of the SMS to have been inappropriate.
The text message was brought to public attention in an article published by newspaper VG last week.
In the message, Giske is reported to have asked the woman whether there was a party at a hotel following a dinner for Labour members.
According to Dagbladet, former Labour Party Youth secretary Tonje Brenna and then-party secretary Raymond Johansen have since discussed the text message after the woman mentioned it to Brenna. No further action was taken and Giske has not been accused of harassment.
After VG last week reported that the message is a source of a current conflict within the party, the woman, now 25, criticised the newspaper's reporting of the situation.
“The only inappropriate and indecent thing I have experienced in connection with this ‘story’ is that journalists, in their search for scandal, go over my head and take away my right to own and define my own story,” the woman, who wished to remain anonymous, told Dagbladet.
On Friday, Labour leader Jonas Gahr Støre told NRK that, based on reports of the message he had read in newspapers Dagbladet and VG, he did not believe Giske had acted inappropriately.
Labour MP Anniken Huitfeldt, who leads the party’s network for female members, also responded to the reports on Monday.
“I do not have knowledge of all aspects of these reports, but I have noted that our party leader said that there was nothing inappropriate in this case. I support his assessment,” Huitfeldt said on NRK's Politisk kvarter programme.
Giske has so far declined to comment on the issue.