“I might have thought about Mengele for 10 minutes,” said Meir Amit, the celebrated chief of Israel’s Mossad from 1963 to 1968.

Amit, who died in Israel a week ago at 88, had made the admission to me in a 1985 telephone conversation, when I was researching a biography on the Angel of Death, Nazi Dr. Josef Mengele.

That a former Mossad chief was so blunt in having little interest in capturing a war criminal charged with personally selecting 400,000 victims to go to their deaths in Auschwitz’s gas chambers, and for brutal medical experiments he did on twins there, was initially startling. But the more we talked, the easier it was to understand why Amit did not mind being known as the Israeli spy chief who let Mengele get away.

“We were fighting for the survival of the state of Israel,” Amit told me. “We didn’t have the luxury of going after Nazis anymore.”

The Mossad’s greatest success in hunting Nazis was the May 11, 1960 capture of Adolf Eichmann, the emotionless bureaucrat responsible for deporting millions of Jews to the concentration camps.

The daring raid in Buenos Aires, conducted by a small team of Mossad agents in an unfriendly, then pro-Nazi country, sent shock waves through the surviving cabal of Nazi fugitives. Mengele, remarkably living under his real name in Argentina, fled to Paraguay and then a year later to the Brazilian outlands .

The Mossad, led by Isser Harel, had convinced then Israeli Prime Minister David Ben-Gurion that capturing Nazis was a proper role for Israel’s spy agency. The Eichmann operation was so costly that Harel wanted to make it worthwhile by picking up Mengele at the same time. But the Israelis couldn’t pinpoint the elusive doctor’s whereabouts, missing him at a boarding house and at Mengele’s own small garage-workshop that made children’s toys.

But Mengele’s fears of the Israelis were well placed. Harel and the Mossad formed “Operation Mengele,” and for more than two years a special team tracked him. Mengele was the top of the Mossad’s list, but Harel had a Parisian-based team chasing other Nazis—from Klaus Barbie, the Butcher of Lyon, to determining whether Hitler’s deputy, Martin Bormann, had really died trying to flee Berlin in the closing days of the war or was living in a guarded compound in the Paraguayan Chaco.

From the spring of 1961 to the end of 1962, several Mossad agents who had worked on the Eichmann team traveled to Europe and South America to penetrate Mengele’s family and Nazi sympathizers in the Odessa, a group that protected Third Reich fugitives. The Mengele team was headed by Zvi Aharoni, an Israeli agent I extensively interviewed. His unit adopted a variety of cover identities: One agent was a financial consultant, another a historian writing a book on the SS.

The Mossad spent more money on Operation Mengele than it had in capturing Eichmann—who was hanged in Israel on May 31, 1962. But it made major inroads. By shadowing Hans Rudel, Hitler’s most decorated pilot and a Mengele acquaintance, as well as capturing a wanted SS officer, Wilhelm Sassens, and squeezing him for information, the Israelis developed key clues about Mengele’s safe houses and his protectors.

Aharoni staked out a Brazilian farmhouse owned by an Austrian neo-Nazi, Wolfgang Gerhard. One day, in mid-1962, Aharoni was himself doing surveillance when three men from the farm strolled past him. He managed to surreptitiously take a picture of them. And he was confident from earlier SS photos that one was Mengele. Aharoni flew to Paris and told Harel he thought he had located Mengele and the covert operation to seize the Nazi fugitive should be activated.

Instead, Harel surprised Aharoni by pulling him and the rest of the Mengele team to Operation Tiger, an effort to find a 10-year-old boy who had been kidnapped by his Orthodox grandparents because they didn’t think his parents were giving him a strict enough religious upbringing. For two years, Israel had been transfixed by the case of missing Yoselle Schumacher. The Mossad had been recruited into the hunt. And Harel used all his resources to infiltrate the almost Mafia-like secrecy of the most secret Orthodox sects to run the boy to ground in New York in July 1962.

Aharoni went back to Harel and said, “Now Mengele?”

“First the rocket scientists,” Harelsaid.

Only days after Schumacher had been returned to his parents in Israel, Egypt’s belligerent president, Gamal Abdel Nassar, successfully test-launched four rockets with ranges up to 350 miles, putting all of Israel at risk. Former Nazi rocket scientists were working on the Egyptian rocket program. Harel launched a letter-bombing campaign to those German scientists who did not heed his anonymous letters warning them to return to Europe. Five were killed. One was seriously injured. Several assassination attempts failed. In the middle of 1963, Harel resigned in a bitter clash with Ben-Gurion over whether the Mossad should continue to kill the Germans.

Harel’s departure created the opening for General Amit, a tough general with a distinguished career, who had been chief of military intelligence. He blamed the surprise of the Egyptian rockets on Harel’s failure to utilize his money and manpower to gather intelligence on Israel’s Arab neighbors.

“I wish we had the money and manpower to have done it all,” Amit told me. “But we were fighting for the survival of the state of Israel. We didn’t have the luxury of going after Nazis anymore.”

The shame is that Amit and the Mossad did what spooks do with information they gather. They locked it up, stamped it classified, and never shared it with any other intelligence agency, private Nazi hunter, or police organization like Interpol. So the one major break in the case about Mengele’s whereabouts stayed buried for decades in a dusty file in Mossad’s headquarters. And meanwhile, Hollywood films like Boys from Brazil and Marathon Man created the image of a bionic Mengele, surrounded by killer dogs and armed guards, methodically creating a biological Fourth Reich with the plundered millions he had taken in escaping from Europe. Instead, the hunt for Mengele became a cold case. The real Mengele lived a simple life, on isolated farms and then in a rundown neighborhood in Sao Paulo, before dying of a stroke while swimming in the ocean, in 1979, at the age of 68.

“Do you ever have any regret that you did not make a greater effort to capture Mengele, that he got away,” I had asked Amit.

“I think I was right then and I think I am still right today.”

Gerald Posner is The Daily Beast's chief investigative reporter. He's the award-winning author of 10 investigative nonfiction bestsellers, ranging from political assassinations, to Nazi war criminals, to 9/11, to terrorism. He lives in Miami Beach with his wife, the author Trisha Posner.