JERUSALEM — The remains of an Israeli soldier who went missing nearly 37 years ago in a calamitous battle with Syrian forces in Lebanon have been repatriated, the Israeli military said Wednesday, healing a long-festering wound to the national psyche and handing Prime Minister Benjamin Netanyahu a unifying achievement just six days before he seeks re-election.

The soldier, Sgt. First Class Zachary Baumel, a 21-year-old tank driver who was born in Brooklyn, emigrated to Israel with his family in 1970. He was lost and believed killed a few days into the 1982 Israeli invasion of southern Lebanon, in the chaos after his brigade was ambushed near the village of Sultan Yakoub, in the eastern Bekaa Valley.

Israel’s military and intelligence services never stopped searching for him, and two others who remain missing. One key breakthrough came in 1993, during the Oslo peace talks, when half of an identification tag belonging to Sergeant Baumel was delivered by Yasir Arafat, the Palestine Liberation Organization chairman, to an emissary of Prime Minister Yitzhak Rabin.

In 2016, Russia returned to Israel, at Mr. Netanyahu’s request, a tank that had been seized in the Sultan Yakoub battle, sent by Syria to Moscow and kept on display at the armored corps museum there.