Opposition Leader Tony Abbott has demoted his policy director after the staffer allegedly told the chief executive of an Indigenous education organisation he would "cut his throat" if the Coalition wins the election.

News Limited journalist Peter van Onselen said he was at a Qantas party in Sydney on Thursday night when he overheard the staffer, Mark Roberts, make the threat.

Dr Roberts was speaking to Andrew Penfold, a former investment banker who is now chief executive of the Australian Indigenous Education Foundation.

I have heard some threats in my time, but nothing like that from an Abbott staffer tonight. Watch this space, I'll raise it on Sunday... - Peter van Onselen (@vanOnselenP) April 19, 2013

A Tony Abbott staffer told an eminent Australian that he would "cut his throat" once "we" are in government.... Much, much more to it... - Peter van Onselen (@vanOnselenP) April 19, 2013

...I am totally disgusted. He is a very senior member of the staff. - Peter van Onselen (@vanOnselenP) April 19, 2013

Van Onselen said Dr Roberts knew he had heard the threat and offered to leak information from Mr Abbott's office in exchange for his silence.

Abbott's staffer knew I heard the conversation, bailed me up & offered to be a source inside TA's office if I stayed quiet...thanks, but no. - Peter van Onselen (@vanOnselenP) April 19, 2013

Mark Roberts Tony Abbott's director of policy

Tony Abbott's director of policy Promoted to position in March 2011

Promoted to position in March 2011 Has doctorate in international economics Andrew Penfold Chief executive of Australian Indigenous Education Foundation

Chief executive of Australian Indigenous Education Foundation A former finance lawyer and investment banker

A former finance lawyer and investment banker Was a finalist for Australian of the Year in 2010

Was a finalist for Australian of the Year in 2010 Nominated by The Australian for its Australian of the Year award in 2012

Earlier today Mr Abbott denied his staffer had made the "throat-cutting" comment but confirmed that an "unfortunate exchange" had occurred.

Mr Abbott said the matter was out of character, the incident had been investigated and he believed the matter was "now ended".

But this afternoon Mr Abbott has been forced to demote Dr Roberts, saying his policy director's comments were "completely unacceptable".

But while Dr Roberts loses his title as policy director, he will continue to advise on portfolios.

Mr Abbott's office will not say if the demotion means a pay cut.

Van Onselen tweeted earlier his amazement that Dr Roberts had denied making the "throat-cutting" comment.

Wow the staffer in Tony Abbott's office is denying the form of words that he used. A number of people heard it so that's interesting. — Peter van Onselen (@vanOnselenP) April 19, 2013