Oklahoma City center Enes Kanter said Monday he routinely received death threats for criticizing the government of his native Turkey, and he may seek an expedited process toward becoming a U.S. citizen.

Kanter was detained at an airport in Romania over the weekend, with border police there saying they did so because Turkish authorities canceled his passport. Kanter eventually was allowed to leave for London and then New York, after he said officials from the U.S. Department of Homeland Security and others intervened on his behalf.

Kanter held a news conference in New York on Monday and said he...