TEL AVIV—Israel’s intelligence services are preparing to kill Hamas leaders around the world when the nation’s war in the Gaza Strip winds down, setting the stage for a yearslong campaign to hunt down militants responsible for the Oct. 7 massacres, Israeli officials said.

With orders from Prime Minister Benjamin Netanyahu, Israel’s top spy agencies are working on plans to hunt down Hamas leaders living in Lebanon, Turkey and Qatar, the small Gulf nation that has allowed the group to run a political office in Doha for a decade, the officials said.