The Oklahoma City Thunder center tweeted a video saying he was being held by police at the airport.
"They said (Turkey's embassy) canceled my passport. They've been holding us here for hours," Kanter says in his video, panning over to two men in white shirts, "by these two police."
A Romanian border police spokesman confirmed Kanter had been stopped but said the basketball player was never detained and had been free to move about the airport, until he left on a flight for London.
He arrived Sunday in New York, according to his verified Twitter account.
, who turned 25 on Saturday, said Ankara had canceled his passport because of his political views and that Turkish President Recep Tayyip Erdogan was responsible.
Reporting on Kanter's tweets, Turkish state media outlet Anadolu said Kanter is a supporter of cleric Fethullah Gulen, an Erdogan opponent who now lives in Pennsylvania. Anadolu's report did not include comment from the Turkish government.
Erdogan recently visited Washington, where he met with US President Donald Trump. During his US visit, violence erupted outside the Turkish embassy
and nine people were hospitalized.
"(Erdogan) is a bad, bad man," Kanter says on the video. "He's a dictator and the Hitler of our century."
CNN reached out to Turkish officials Saturday afternoon, which was early Sunday in Turkey, but has not yet received comment.
Kanter later tweeted that he was doing well and would speak to the media in New York on Sunday.
"All good, baby!" he wrote. "Got lots of things to say with lots of crazy stories."
Romanian official: Kanter not held
In his video, Kanter, who appears to be in a terminal waiting area, asks for prayers for his situation.
Fabian Badila, a spokesman with the Romanian Border Police, told CNN that Kanter arrived in Bucharest around 1 p.m. from Frankfurt, Germany.
Border control agents established through computer records that Kanter's travel documents were not valid.
"They were canceled by the Turkish government," Badila said. "Romanian law says you can't cross the border if you don't have valid travel documents."
He said Kanter was not held in custody. "He was not detained. He was free and walked around the airport."
Kanter posted two photos of himself posing with the officers at the airport.
The 6-foot-11 center has been in the NBA for six seasons with the Thunder and Utah Jazz. This season he averaged 14.3 points and 6.7 rebounds in 72 games. In 2011 he played for the Turkish national team in European championships, according to NBA.com.
The Thunder, whose season has ended, said: "The Oklahoma City Thunder are working with the NBA to gather more information through the appropriate channels."
Kanter's Facebook page indicates he is on a not-yet-concluded tour on behalf of his foundation. The page refers to his visit to Bucharest as stop No. 8.