Fairfax Media has reported Mr Heydon was part of the seven-member Rhodes Trust selection committee in NSW that in 1980 approved a Rhodes scholarship for Mr Abbott, who was then a student at Sydney University.
"That's a long time ago and the idea that I gather is being peddled that somehow he and I cooked up a conspiracy 34 years ago against the Labor Party is absurd," Mr Abbott told reporters in Canberra on Monday.
Pressure is mounting on Dyson Heydon to stand down as head of the royal commission into union corruption, amid controversy over a scheduled appearance at a Liberal party event.
Unions accused of ‘grand-standing’
Earlier, trade unions were accused of grand-standing after the ACTU asked for want more time to consider whether to take action to remove the royal commissioner.
ACTU secretary Dave Oliver told reporters outside the commission hearing in Sydney that lawyers needed time to review a series of emails which indicate Mr Heydon was aware as early as April 2014 that an event he had agreed to address was being organised by the Liberal Party.
"We have a genuine concern that he appears to be biased and we would expect commissioner Heydon to give the unions time to consider the evidence and time to determine what our next course of action should be," he said.
Trade unions have been accused of "grandstanding" after the ACTU sought more time to consider documents that may lead to Dyson Heydon having to disqualify himself as the head of the royal commission into union corruption.
Mr Heydon had given senior counsel Robert Newlinds an hour to seek instructions from his clients after they were provided with a series of emails about the commissioner's initial decision to speak at a Liberal Party event.
After Mr Newlinds asked to be excused for the day to continue discussions, counsel assisting the commission Jeremy Stoljar said the hearing was "descending into a shambles".
"It smacks of grandstanding," Mr Stoljar said.
Mr Newlinds rejected the criticism.
"The last thing I have tried to do is to grandstand and make this a farce," he said.
He said the documents had only been provided on Monday morning and he would need up to a week to take further advice.
Mr Heydon gave Mr Newlinds until 4pm on Monday and the commission adjourned.
Earlier the commissioner admitted he had "overlooked" a connection between the Sir Garfield Barwick address and the Liberal party.
"My understanding at all times has been that the dinner was not to be a fundraiser," he said.
Mr Heydon said his acceptance in April 2014 was conditional on the commission having wrapped up its business before 2015.
The federal government in October 2014 extended the commission's term by one year.
In parliament, Prime Minister Tony Abbott described Mr Heydon as professional and impartial.
He said that after Mr Heydon became aware the lecture was to be at a Liberal-badged event, he withdrew.
The prime minister told reporters he couldn't recall if Mr Heydon was on the panel that selected him for a Rhodes scholarship in 1980 when he was a Sydney University student.
"That's a long time ago and the idea that I gather is being peddled that somehow he and I cooked up a conspiracy 34 years ago against the Labor Party is absurd," he said.
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