"To sum it up in a phrase, there's no fool like an old fool," Peters said.
Peters backed up his allegations on Q&A this morning, saying Dunne was "leaking like a sieve".
Asked if Dunne leaked stories to Vance, Fairfax executive editor Paul Thompson said: "We never talk about our confidential sources. I have no comment whatsoever to make, we won't be going anywhere near that."
At Friday's press conference where he stood down as a minister, Dunne said his relationship with Vance was completely professional.
Asked about his relationship with the former News of the World reporter, Dunne replied: "There is absolutely nothing in that rumour. My relationship with Andrea Vance was professional as is my relationship with any other journalist."
He said he had planned to meet Vance for coffee after he returned from a holiday with his wife.
"I headed off in the direction of meeting her but never actually got there. I ended up meeting people and then time slipped away, I picked up lunch and went back to the office."
Asked why he wanted to meet her, he said he had been away for 10 days and wanted to "catch up".
A report by retired public servant David Henry showed Dunne and Vance had 64 email exchanges while Dunne was in America with his wife between March 30 and April 7. The pair also tweeted often.
As a minister outside Cabinet, Dunne was privy to a lot of classified information. Peters claims he has copies of "electronic communications" between Dunne and Vance that indicated he leaked to her on at least four other occasions:
• An internal GCSB survey showing staff morale at the spy agency had "declined dramatically" (October 16, 2012).
• Novopay payroll system undermining Inland Revenue's payment of teachers' child support and KiwiSaver contributions (February 5, 2013).
• Details of the Prime Minister's involvement in the appointment of his old schoolmate Ian Fletcher as head of the GCSB (April 2013).
• The resignation of National MP Jackie Blue to take up the position of Equal Opportunities Commissioner (April 16, 2013).
Peters refused to expand on the nature of the electronic communications he had obtained - emails, text messages, tweets or other mediums - but he insisted he had more than just the publicly available Twitter exchanges between the minister and the reporter.
Dunne has admitted canvassing the possibility of leaking the GCSB report with Vance but denied actually leaking it.
He tendered his resignation on Friday, after refusing to supply copies of 86 emails between himself and Vance. Instead, he surrendered edited summaries of 41 emails he had sent to her. He refused access to three more emails he had sent her, as well as the 42 emails she sent him.
Political commentator Bill Ralston said yesterday it was unclear whether there was anything other than a typical reporter/politician relationship between Vance and Dunne.
"It is obvious Peter Dunne was very interested in talking to her frequently and she was replying to him. You can't tell if it was a professional relationship or something else."
