Rafi Eitan, who commanded the audacious capture in 1960 of top Nazi Adolf Eichmann in Argentina, said that during the hunt he and his team discovered Mengele's hideout.
"At the same time as we caught Eichmann, Mengele was living in Buenos Aires. We found his apartment and kept it under observation," he told Israeli public radio as the spy agency declassified its file on operations against the man known to prisoners as the "Angel of Death".
Yediot Aharonot newspaper, citing the newly available material, said that Mengele as chief medical officer at Auschwitz had "sent hundreds of thousands of Jews to the gas chambers with a wave of his hand".
"He also directed shocking 'medical' experiments on prisoners," it wrote.
Eitan, 90, said that while the Mossad had Eichmann in a safe house ahead of smuggling him out of Buenos Aires in an El Al plane, the agency's chief, Issar Harel, wanted them to move against Mengele as well, but he argued against the plan.
"I didn't want to carry out two operations at the same time because we had one succesful operation in the bag, and in my experience if you try to carry out another one you put them both at risk," Eitan said.
As a compromise he stayed on in Argentina to keep tabs on Mengele, while his teammates took Eichman, as the main architect of the Nazi Holocaust, back to Israel, where he was later tried and hanged.
"Mengele wasn't at home and the neighbours said he would be back in a week," Eitan continued.
"We waited a week but in the meantime his (Eichman's) capture was announced to the world and Mengele never returned to his apartment in Buenos Aires."
The Mossad team missed him again when he was spotted in Brazil, Eitan added.
"At the end of 1962 Mengele was positively identified at a farm near Sao Paulo."
But Mossad chief Issar Harel resigned early the next year and his successors did not approve an operation against Mengele as they had other priorities around the world, he said.
Mengele died in a drowning accident in Brazil in 1979.