Mr Carter apologised to Vance and her employer, Fairfax, but said the phone records had neither been sought by Mr Henry nor used in the inquiry.
He said Mr Henry had recorded that fact immediately that the information was received.
"We all have a love-hate relationship with our Press Gallery," Mr Carter said during a parliamentary debate on Parliamentary Service's budget, "but they are an absolutely essential part to this democracy.
"There has been a breach of trust that has occurred and I will do all in my power to get to the bottom of it."
A company contracted by Parliamentary Service to operate Parliament's phone system supplied the information to the inquiry.
"This private information should not have been released and could be seen to attack the freedom of the press," Mr Carter said, "which is critical to informing the public about what Parliament is doing and ensuring public confidence in Parliament. I view any actions that may put at risk journalists' ability to report freely very seriously."
Greens' Russel Norman: It's no mistake
Greens co-leader Russel Norman told Radio NZ there were conflicting accounts over what had happened, but he did not accept Mr Carter's explanation that the records had been handed over by mistake.
"We have two pieces of evidence to contradict that - the first is Mr Carter's original answer to my written question, which said that the Henry inquiry did request the report ... the second piece of evidence is Mr Dunne's account of his conversation with Mr Henry.''
Dr Norman said that account was "strongly suggestive'' that the inquiry already had access, or was intending to get access, to Ms Vance's phone logs.
He said a Parliamentary privileges committee should try to find out what had happened, then develop guidelines and very clear rules so "this kind of thing never, ever happens again''.
Dr Norman said there were two key constitutional issues at play - firstly, that the executive branch of government had no right to impinge on the parliamentary branch of government, and secondly, that it had no right to impinge on a free press.
The privileges committee has been commissioned to look into the issue further, and into who is entitled to access information about journalists' and MPs' communications.
Key "troubled by this news"
Mr Key said in his letter to Mr Carter that on finding out that Parliamentary Service had voluntarily supplied the journalist's phone records "I was deeply concerned and troubled by this news".
"I believe it is inappropriate for such information to be provided to the inquiry and I wanted to convey this view to you in writing."
Mr Key has been under attack over the GCSB bill which will expand the legal powers of the spy agency.
He is on the defensive over his association with an inquiry that overstepped what was expected of it.
Dunne: Inquiry "sicker by the day"
United Future leader Peter Dunne, who was forced to resign for not co-operating with the inquiry, said last night the inquiry was "sicker by the day".
Mr Dunne, however, has raised questions over Vance's phone records.
Mr Dunne said he had several meetings with Mr Henry and said that at one of them Mr Henry had sought his landline phone records from March 27 to April 9 and which he handed over.
"He ... gave me the impression he wanted to compare the records."
Ex-TVNZ head of news: "It's outrageous"
TVNZ's former head of news, Bill Ralston, added his voice to the chorus of media figures who have condemned the records being handed over.
"It is frankly outrageous that Parliamentary Service should access the phone information of any private individual, let alone a journalist,'' he told Radio New Zealand this morning.
Ralston said if it was a plot against the media, it was a "very poorly executed conspiracy''.
"I tend towards the incompetence end of the scale here.''
Ralston said it was clear that someone within Parliamentary Service instructed a contractor to hand over the information, and heads should roll over the initial mistake and the "internal cover-up''.
He said it was extremely hard for the Press Gallery to do its job if it was completely under Government surveillance.
"It is almost impossible to do your job in any other way, other than attending press conferences, because you cannot find out what's happening behind the scenes if you know you're being watched.''
