Mr Dunne had written to Parliament's Speaker of the House, David Carter, seeking his assurance that the emails were not accessed during that time.
A week after the emails were posted on the parliamentary server - which Mr Dunne believes means they were accessible to others within the complex - NZ First Leader Winston Peters claimed Mr Dunne was responsible for the GCSB leak.
Mr Peters subsequently said his claim was based on his knowledge of the emails between Mr Dunne and Ms Vance but yesterday he refused to confirm whether or not he had accessed the file.
Mr Dunne told reporters Mr Carter had advised him Parliamentary Service was now doing more detailed work to determine whether they were accessed, and if so by whom.
However, he didn't believe Mr Peters' claim he'd seen the emails.
"I've challenged him before to put up or shut up, and every time it's fallen on deaf ears ... I suspect it's all bluff."
However Prime Minister John Key had little sympathy for him, saying yesterday that no minister, including Mr Dunne, complained about the inquiry's terms of reference.
The inquiry list grows
• The Kitteridge Inquiry into the GCSB's compliance with relevant law
• The Henry Inquiry into the leak of the Kitteridge report
• Privileges Committee hearings into the conduct of the Henry Inquiry
• Speaker David Carter's inquiry into whether Peter Dunne's emails were subject to unauthorised access