The Labour leader was left to defend the remarks made at the time and insisted he merely thought “a negotiated solution” through the UN was necessary.
He reportedly said at the time: “The whole thing is a Tory plot to keep their money-making friends in business.”
Mr Corbyn replied: “I don’t think they should have gone in there but I also think there should have been an opportunity to prevent that war happening by the UN, which was being attempted at that time.”
Probing further, the presenter added: “So you do think it was a Tory plot, do you?”
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Jeremy Corbyn was roasted by Jeremy Paxman on his stance on the Falklands War
I felt that she [Margaret Thatcher] was exploiting the situation but there has to be at the end of every conflict, there has to be a peace process
The Labour leader denied the claim and insisted he thought there should be a negotiated solution through the United Nations.
But Paxman continued to roast Mr Corbyn over the remarks. He asked: “If you didn’t believe it was a Tory plot, why did you say you thought it was?”
The politician then said he thought Margaret Thatcher was “exploiting the situation”.
He replied: “Jeremy, Margaret Thatcher made a great deal of the whole issue as everybody could see at the time.
“I felt that she was exploiting the situation but there has to be at the end of every conflict, there has to be a peace process.
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Snap election 2017: The pictures politicians may not want you to see Sat, May 27, 2017
Protests, fights and daleks, it's all happening as the politicians hit the campaign trail for the snap election
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Jeremy Corbyn during a visit to Hackney Marshes Football Pitches, to highlight Labour's manifesto commitment to ensure 5% of the Premier League's television rights income is diverted to the grassroots game, during a General Election campaign
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Jeremy Corbyn said Margaret Thatcher had "exploited the situation"
“Why don’t we start with the objective of trying to get a peace process and use our councils through the United Nations to achieve that?”
The host then lambasted Mr Corbyn over what he would do over any future conflict.
He responded: “Because it’s quite possible that in a couple of weeks time if you’re sitting in Downing Street, the chief of the defence staff could come to you and say we have eyes on a man in Iraq or in Syria or in Afghanistan who is plotting a bombing campaign in Britain.
“You have 20 minutes to make up your mind as to whether we take him out with a drone strike. Do you think that’s a Tory plot as well?”
But Mr Corbyn insisted he would want to know the circumstance and the evidence and what the effect would be on civilians before making any decisions.