The messages, which span November 3 to November 23, show Curran was "keen to catch up soon" with Hirschfeld.
The meeting at the busy Astoria cafe in central Wellington led to the resignation of Hirschfeld yesterday.
Curran said she had no intention of resigning as Broadcasting Minister.
The women exchanged "a handful" of texts in the days leading up to the meeting in December last year.
The minister's spokeswoman confirmed that Curran initiated the meeting.
Curran, the MP for Dunedin South and also Minister for Open Government, said she had no intention of resigning over the meeting, saying again that her only mistake was failing to disclose the meeting in her original answer to a parliamentary question on December 7.
The texts reveal Curran had repeatedly tried to set up a meeting with Hirschfeld from November 3, just days after she was sworn in as Broadcasting Minister on October 26.
After a back and forth on availability and dates, they settle on December 5. Curran suggests the time of 8.15am at a venue "somewhere near Bowen House entrance off Lambton Quay", Curran then suggests Astoria.
"Perfect," Hirschfeld replies.
Curran's spokeswoman declined to say who in Curran's office contacted RNZ to correct Hirschfeld's assertion that it was a chance encounter, or who at RNZ had been contacted.
Hirschfeld's resignation on Tuesday followed four months of her denying that the meeting was arranged.
Hirschfeld repeatedly told RNZ bosses for four months that the meeting was a chance encounter, despite it being recorded in the minister's diary for five days before the meeting, and two attempts by the minister to tell RNZ that Hirschfeld was wrong.
Curran says she won't resign saying it wasn't a secret meeting as it was in a public, busy cafe.
She described the meeting as a catch-up between friends.
They discussed the future of RNZ, including the announced $38 million in Government spending, and "high level" discussions about RNZ+.
The whole episode unravelled yesterday with Hirschfeld's resignation as head of RNZ content, Curran's admission of wrongdoing, and Opposition leader Simon Bridges questioning Curran's integrity.
"It's hard for New Zealanders, frankly, to believe a word she says," Bridges said.
The issue became political after Curran said the meeting was "unofficial" and excluded it from a list of meetings that she provided in response to a parliamentary question.
On Tuesday she said she made a mistake and should have included it from the beginning.
Prime Minister Jacinda Ardern stood by Curran, saying she had corrected the record - though it had taken two and a half months and she should have done it sooner.
Curran remains in the spotlight for what was said in the meeting and whether it could be seen as an attempt to influence the editorial direction of the state broadcaster, which is about to get a large portion of $38 million in Government funding to set up RNZ Plus.
Curran called it a "high-level discussion" about the state of the media and RNZ's future, and a spokeswoman last night insisted that "the minister was not trying to push RNZ in any direction".
Ardern also said that Curran had assured her that there was nothing inappropriate in her discussion with Hirschfeld.
Curran also defended her decision not to set the record straight publicly after she found out on March 1, after a select committee meeting with RNZ bosses, that Hirschfeld was calling it a chance encounter.
She said her office contacted RNZ immediately to correct Hirschfeld. "It then became a matter for RNZ to deal with."
RNZ bosses questioned Hirschfeld about the matter again, who reassured them it was a chance meeting.
Curran said her office again contacted RNZ this week to say it was an arranged meeting. On Sunday, Hirschfeld admitted the meeting was pre-planned, leading to her resignation yesterday.
Curran said she may have been naive to hold the meeting, and would not have held it if she had known about RNZ protocols about meetings.
Asked why Hirschfeld persisted in describing it as a chance meeting, Curran said: "You'd have to ask her."
On Tuesday Hirschfeld went to ground but RNZ chairman Richard Griffin and chief executive Paul Thompson said they were "very disappointed".
Based on what Hirschfeld had told them, Griffin and Thompson inadvertently misled a parliamentary select committee on March 1, telling MPs that Hirschfeld had been at the gym when she chanced upon Curran.
RNZ reported this morning that Griffin would be making a statement to the select committee as the last one he provided was based on incorrect information from Hirschfeld.
Committee chairman National MP Jonathan Young was quoted as saying that was appropriate but he needed to discuss the matter with the rest of the committee before deciding how to proceed.
The New Zealand Herald visited Hirschfeld at her Grey Lynn house in Auckland this morning. She was visibly emotional but declined to comment.
