The newspaper cited comments reportedly made by Donald Rickard, a former US vice-consul in Durban and CIA operative, to British film director John Irvin.
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Irvin's new film "Mandela's Gun", about the months before the anti-apartheid icon's arrest, is due to be screened at the Cannes film festival this week.
Mandela was eventually freed from prison in 1990 and went on to become South Africa's president between 1994 and 1999 before dying in 2013 aged 95.
An article by James Sanders, who said he was asked by Irvin to investigate the issue, said the director travelled to the US earlier this year and interviewed Rickard.
Rickard explained how Mandela was arrested as he travelled between Durban and Johannesburg but did not explain how he had learnt where he would be.
"I found out when he was coming down and how he was coming... that's where I was involved and that's where Mandela was caught," Rickard was quoted as saying.
He added that Mandela was "completely under the control of the Soviet Union".
"He could have incited a war in South Africa, the United States would have to get involved, grudgingly, and things could have gone to hell," Rickard added.
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"We were teetering on the brink here and it had to be stopped, which meant Mandela had to be stopped. And I put a stop to it."
Rickard, who was reportedly employed by the CIA until 1978, died in March, two weeks after talking to Irvin.
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