The Prime Minister's department has refused to release emails relating to the public service commissioner John Lloyd and a right-wing think tank, saying they could prejudice an investigation into a possible breach of the law.
Mr Lloyd has previously rejected suggestions he gave special access and research to the Institute of Public Affairs after Labor senators last year raised an email he sent to a member of the group with an attachment showing what he described as "generous" provisions in public service enterprise agreements.
A freedom of information request sought emails held by Department of Prime Minister and Cabinet secretary Martin Parkinson mentioning Mr Lloyd and the IPA, and dated from October 23, after senators referred to the email in a Senate estimates hearing.
The department responded to the request last month by refusing to release two emails in Dr Parkinson's inbox, dated December 20 and December 22.
"I am satisfied that disclosure of the documents could reasonably be expected to prejudice the conduct of an investigation of a breach, or possible breach, of the law in a particular instance," assistant secretary Peter Rush wrote.
Releasing the documents could also "reasonably be expected to prejudice the impartial adjudication of a particular case", Mr Rush said.
One document is 30 pages long, and another is five pages.
The department and the Australian Public Service Commission have refused to answer repeated questions from Fairfax Media asking who is under investigation, who is conducting the probe, and the matters being investigated.
"The department has no comment," Prime Minister and Cabinet said in two separate statements.
The APS commission said it would not comment "on speculation about any investigation".
Prime Minister and Cabinet's freedom of information decision comes after Mr Lloyd agreed in an October Senate estimates hearing to take on notice requests for phone records of his contacts with the IPA.
The commission later said it wouldn't release them to senators because it would involve an "unreasonable diversion" of its resources.
"In addition, it would include the release of personal information that would breach the privacy of Mr Lloyd and the people he has phone contact with," it said.
However the commission confirmed last year that Mr Lloyd met with an IPA representative in April 2015 after sending it an email saying Labor senator Penny Wong had "taken a swipe" at two of the think tank's former directors.
The commission said the meeting had no connection to the commissioner's role, and no notes were kept.
Senators last year questioned Mr Lloyd's IPA links after the public service commission faced criticism over new social media rules against public servants revealing their political opinions.
Workers may face disciplinary action over a private email or for "liking" a social media post.
Mr Lloyd rejected a suggestion at a Senate estimates hearing last year that he provided the IPA "special access" or research, saying the information he sent was publicly available.
"My sense of it is there's nothing untoward there," he said.
He told senators his contact with the IPA was "very infrequent", that it would usually approach him, and said it was appropriate in his role to speculate on the generosity of arrangements in APS enterprise agreements.
The public service commission has previously said Mr Lloyd's email correspondence with the IPA, and his meeting with the institute, upheld the APS value of impartiality.
Before the Abbott government appointed him APS commissioner in 2014, Mr Lloyd was the director of the IPA's work reform and productivity unit.