Rafi Eitan, now an 81-year-old Israeli Cabinet minister, said he and the other Mossad men located Mengele - infamous for conducting horrific medical experiments on inmates - living in a Buenos Aires apartment with his wife. But they decided that trying to nab him would risk sabotaging the capture of Eichmann, whom they deemed more important.
It was known that Mengele was living in Buenos Aires around the time of the Eichmann capture. But Eitan's comments indicated that the Israelis were closer to him that has been thought - and shed light on why they decided to abandon an attempt to catch him.
"When you have one operation, you're taking a certain level of risk. If you're doing a second operation at the same time, you double the risk ... not only for the second operation but for the first one as well," Eitan told The Associated Press on Tuesday.
Mengele was never caught and died in 1979. Eichmann, responsible for implementing Hitler's "final solution," the destruction of European Jewry that resulted in the killing of 6 million Jews, was spirited to Israel, tried and executed.
At the Auschwitz death camp, Mengele was one of those responsible for the selection of incoming prisoners, choosing who was fit for slave labor and who would be sent to their deaths in the gas chambers. He also carried out cruel medical experiments on children, twins and dwarves.
"He would tell little children to sit on his lap and tell them to call him 'uncle,' 'uncle Mengele' and sometimes give them a sweet - and in the same tone of voice that he said 'I'm uncle Mengele,' he would tell the officials to give them a lethal injection," Martha Weiss, a survivor of his experimental ward, told the AP in 2005.
After the war Mengele fled Germany under an assumed name and ended up in Argentina, a popular refuge for many senior Nazi officials.
Informers working with the Mossad had seen Mengele while the agents were in Buenos Aires, Eitan said. The Mossad men located Mengele's apartment, and on one specific day even knew he was at home, Eitan said. But the next day Mengele left with his wife for what the agents believed was to be a temporary absence.
At the time, the Israelis had already snatched Eichmann and were holding him in a safe house while they waited to whisk him out of the country.
Fearing that if they waited for Mengele to come back, the Eichmann operation would be discovered, Eitan decided it was not worth the risk.
"When I have a bird in my hand, I don't start looking for the bird in the bush. I'll take the bird in my hand, put it in a cage, and then deal with the one in the bush," Eitan said.
But by the time the Mossad sent a team back to Buenos Aires a few weeks later, it was too late. "After Eichmann's capture was made public, he disappeared entirely," Eitan said.
Historian Avner Shalev, chairman of Israel's Yad Vashem Holocaust memorial authority, said the Mossad made the right decision under the circumstances, since Eichmann was more important than Mengele. But he said bringing Mengele to justice in Israel would have had great symbolic and educational value.
As a doctor, Mengele represented "the extent of the collapse of the human values built by Western society over the years," Shalev said. "There would have been a universal message that would have benefited the world if Mengele had been put on trial, especially in Israel."
After missing him in Argentina, the Mossad had another shot at catching him in Sao Paolo, Brazil, two years later, Eitan said, but the organization had other "operational priorities," and Mengele got away. He would not say what those priorities were.
Having eluded capture for 34 years, Mengele drowned in Brazil in early 1979. Experts identified the body as his six years later.
Eitan went on to a long career in intelligence that ended on a sour note. He took responsibility for the case of Jonathan Pollard, an American Jew who spied for Israel, was arrested in Washington in 1985 and was sentenced to life in prison, one of the most embarrassing and damaging episodes in Israel-American relations.
After Eichmann was caught, the Mossad considered expanding its activities targeting Nazis, said Efraim Zuroff, a Nazi hunter who heads the Simon Wiesenthal Center's Jerusalem office.
But the organization eventually shifted its resources elsewhere, he said, and Eichmann remained one of only two significant anti-Nazi successes the Israeli secret service had.
The other, Zuroff said, was the assassination of Herberts Cukurs, who headed a Latvian death squad known as the Arajs Kommando that killed 30,000 Jews in Latvia. Mossad agents lured him from Brazil to Uruguay and killed him in 1965, making it look as if he had been killed by survivors taking revenge.
"The Mengele story underscores the tremendous difficulties involved in bringing Nazi war criminals to justice, certainly those living in a country like Argentina, which opened its arms to grant them shelter and protection," Zuroff said.