Story highlights JetBlue apologizes for "computer glitch" that indicated the toddler was on a no-fly list

The family, of Middle Eastern descent, was flying from Florida to New Jersey on Tuesday

TSA spokesman says agency "did not flag this child as being on the no-fly list"

The family declined to continue on the flight; the father says they felt humiliated

JetBlue Airways is apologizing for a "computer glitch" it blames for a family being told their 18-month-old daughter was on a government no-fly list.

The parents, who reportedly would not disclose their last names for fear of repercussions, and their infant, identified only as Riyanna, had boarded JetBlue Flight 510 from Fort Lauderdale, Florida, to Newark, New Jersey, on Tuesday evening when they say an airline employee ask them to get off the plane.

"I said, 'For what?'" Riyanna's mother told CNN affiliate WPBF. "He said, 'It is not you or your husband. Your daughter was flagged as no fly.'"

The family is of Middle Eastern descent and the mother wears a headscarf, but they say they are U.S. citizens and have lived in New Jersey all of their lives.

The government disputed the airline's initial characterization.

"TSA did not flag this child as being on the no-fly list," Transportation Security Administration spokeswoman Sterling Payne told CNN in a statement. "TSA was called to the gate by the airline and after talking to the parents and confirming through our vetting system, TSA determined the airline had mistakenly indicated the child was on a government watch list."

The family declined to continue on the flight, saying they felt humiliated.

"We were put on display like a circus act because my wife wears a hijab," Riyanna's father said.

The airline says it was a technical mistake.

"We are investigating this particular incident. We believe this was a computer glitch," JetBlue Spokeswoman Allison Steinberg said in a statement without elaborating. "Our crewmembers followed the appropriate protocols, and we apologize to the family involved in this unfortunate circumstance."

"The whole situation was bizarre, it was completely bizarre and absolutely made no sense," the mother added.

Steinberg said JetBlue crew members "are trained to address each situation discreetly, treating every customer with dignity and respect."

The government maintains several databases of individuals who warrant extra screening when they fly. No one on the official no-fly list would be given a boarding pass, according to a TSA official who did not want to be named discussing the matter.

About 20,000 people are on that list, according to a counterterrorism official, including 500 Americans.