KUALA LUMPUR, Malaysia—Malaysia deported three Turks back to their homeland, raising concerns that Ankara is enlisting foreign governments to help crush a movement that President Recep Tayyip Erdogan blamed for a failed coup last year.

National Police Chief Khalid Abu Bakar said Friday that the men were suspected of being involved in an alleged terrorist organization linked by Ankara to Fethullah Gulen, an opponent of Mr. Erdogan living in exile in the U.S. Tens of thousands of his suspected followers have been purged from...