Burgess made the comments in an address earlier this week where he warned Australia was being targeted by intensified efforts from foreign agents.
He alleged that one former politician had been successfully recruited.
Pressure has since mounted on ASIO to reveal that ex-politician’s name, though Burgess has said the case is historical and the individual is no longer a security threat.
Opposition leader Peter Dutton this morning backed calls for the individual’s name to be revealed, though he also urged the country to focus on the underlying message from Burgess that foreign interference was at an “unprecedented” level.
“But I think in a circumstance where you make an allegation or a suggestion like this, I think it is important for public confidence to know who it is,” he told Today.
“Also because 99 per cent of people on both sides of politics are good people, they serve our country, and if there’s one person that he’s talking about who is in scope here, then I think that person should be outed.”
Independent MP Dai Le also called for the release of the individual’s name.
“It’s kind of really smearing that any form of politicians or even any politician currently in Parliament, right?” she told Today.
“So I would be urging ASIO to really name because that has huge ramifications for our democratic and political system.”
However, NDIS Minister Bill Shorten said politicians should not “play prosecutor” and trust Burgess’ handling of the matter.
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ALP president Wayne Swan also told Today the public should trust in ASIO’s operational reasons for discretion in this case.
Burgess has said his decision to not name the individual is due to his unwillingness to disclose ASIO’s methods of exposing foreign agents.