In the winter of 1966, Mr. Sagi’s commanders sent him on a secret mission, via Israel’s then-ally, Iran, to aid Mullah Mustafa Barzani and his pesh merga rebels in Iraqi Kurdistan. Six Iraqi army brigades were standing by to overwhelm the Kurds when the snow melted. Mr. Sagi, a lieutenant colonel, drew up defenses for Barzani’s lightly armed fighters. When those collapsed, Mr. Sagi advised the Kurds to allow the best of the Iraqi brigades to break out — right into an ambush.

The 5,000-man Iraqi brigade was wiped out, and the battle, on Mount Handrin, became a landmark in Kurdish history. Mr. Sagi recalls Iraqi officers driving up in two jeeps waving white flags.

“They said to the Kurds, ‘What do you want?’” he recalled.

Over the years, Israeli doctors set up a field hospital for the Kurds, its soldiers trained the pesh merga fighters and the Mossad helped arm them.

After Israel’s defeat of its Arab neighbors in 1967 and the Baathist coup in Iraq a year later, Iraq became inhospitable to its dwindling Jewish population. Then it was the Barzanis’ turn to help.

After nine Jews were hanged in Baghdad’s Tahrir Square in 1969, Iraqi Jews were desperate to flee. The Kurds helped some 1,000 of them escape, over land to Iran and then by plane to Israel.