BRUSSELS—Apple Inc. Chief Executive Tim Cook issued the tech giant’s strongest call yet for U.S.-wide data-protection regulation, saying individuals’ personal information has been “weaponized.”

Mr. Cook’s call came in a sharply worded speech before a privacy conference organized by the European Union, which in May enacted the General Data Protection Regulation in a bid to both improve user rights and bolster the 28-member bloc’s power as a global rule-maker. Mr. Cook told the audience of EU privacy regulators that the U.S....