"To be greeted like this because of my name, it took me back a little bit," said Jackson, who is black.
Israel is the first stop on a six-nation tour celebrating the New York-based dance company's 50th anniversary. Earlier this year, Congress passed a resolution calling the Alvin Ailey American Dance Theater a "vital American cultural ambassador to the world."
Jackson said he was pulled aside from other members of the troupe when they arrived at Israel's international airport on Sunday night. He said he was taken to a holding room, where he was asked about the origins of his name. When he explained he was part of the dance group, he was asked to perform.
"I stood up. I asked what type of dance?" he explained. "He said, "Just do anything.' I just moved around."
Minutes later, he said a female officer put him through a similar interrogation and asked him to dance again.
"The only time I'm really expected to dance is when I'm performing," he said.
Jackson said he received his name because his father was a convert to Islam. Jackson said he was not raised a Muslim, does not consider himself religious and is engaged to a Jewish woman in the troupe who has relatives in Israel.
Jackson said he did not plan to press the matter further, saying the numerous apologies he has received from American dignitaries and his Israeli hosts is "enough for me." The Israel Ports Authority said it had no comment because it did not receive a formal complaint.
The incident was reported in Israel's largest newspaper and on an Israeli television news and interview program. "The security guards should be sent home or (the airport) will become a mental asylum," said Motti Kirshenbaum, a veteran commentator and host of the Channel 10 TV program.
Israel is constantly on the alert for attack because of the Israel-Palestinian conflict and extremist Islamic rejection of the Jewish state's existence. Security is strict at all entry points and inside the country.
Israel is famous for the effectiveness of its airport security. But a key element in its security checks is ethnic profiling. The practice has been criticized by Israeli human rights campaigners as racist because it singles out Arabs for tougher treatment.
Such profiling is illegal in the United States, but Jackson said that the only place he has had the similarly humiliating experience of being forced to dance in the past was at a U.S. airport when he returned from a vacation in the Dominican Republic. He did not say when or where that took place.
Jackson said that since the Israeli airport incident, the reception in Israel has been "amazing."
"We're only here to bring positive light to our lives and the people here," he said, calling the group's multicultural appeal "an amazing bind you can't touch, you can only experience."