A Turkish educator in Mongolia was briefly abducted on Friday, in what appeared to be the latest episode of a global campaign by Turkey’s president to capture suspected allies of the exiled cleric accused of plotting a 2016 coup attempt.

The educator, Veysel Akcay, runs a network of international schools that has been associated with the exiled Turkish preacher Fethullah Gulen. President Recep Tayyip Erdogan, who blames Mr. Gulen for the failed coup, has purged tens of thousands of suspected Gulen supporters from government and military posts, and seized dozens of people from abroad.

Turkey has maintained that it extradites suspected Gulenists only with the permission of the foreign governments concerned. But the case of Mr. Akcay, who has lived in Mongolia for nearly 25 years, appears to cast doubt on that claim.

Mr. Akcay was near his apartment building in the capital, Ulan Bator, on Friday morning when he was bundled into a Toyota minivan, according to a colleague, Ganbat Batbuyan, who was in communication with the Mongolian police. That account was corroborated by two other people, including another colleague and a senior Mongolian official, who spoke on condition of anonymity because they were not authorized to discuss the case.