Romanian Border Police spokesman Fabian Badila confirmed to The Associated Press that the player left Romania for the United States via London.
Kanter, who is from Turkey, said in a video Saturday morning on his Twitter account that the Turkish embassy canceled his passport and he'd been detained for several hours at a Romanian airport.
Kanter said he believed he was held because of his political views. He's been a critic of Turkish president Recep Tayyip Erdogan. Kanter supports Turkish cleric Fethullah Gulen, who opposes Erdogan.
Romania's foreign minister said on Sunday that his country had no choice in detaining Kanter.
Teodor Melescanu said Romania could not "proceed otherwise" in comments made to news.ro. He declined to comment further.
Kanter has been one of the NBA's best reserves the past two years. This season, he averaged 14.3 points and 6.7 rebounds.