Two Muslim men were removed from a flight bound for North Carolina before the plane took off Friday, reportedly because they were clad in traditional Muslim garb, making the pilot and other passengers uncomfortable.

The two men, Masudur Rahman and Mohamed Zaghloul, are both imams and were headed to a conference to discuss Islamophobia — fear of Islam — and tolerance with other religious leaders.

Rahman compared his plight to the Civil Rights movement, and told a CNN affiliate, "That history I found today in that plane, and it shouldn't happen with any other person," he said.

The men have contacted the Council on American-Islamic Relations, which said the case will be pursued.

Ibrahim Hooper, a spokesman for the group, said that the men had gone through multiple security checks and gotten on the plane, but that the pilot had taxied it back to the gate.

Transportation Security Administration "came on and pulled them off and said the pilot was refusing to fly with them because passengers were uncomfortable with them," Hooper said. Rahman and Zaghloul were re-screened and still didn't present any threat, but the pilot "absolutely refused" to fly them on the plane.

Representatives for Atlantic Southeast Airlines, which operated the Memphis-Charlotte flight, said that the incident was under investigation, and that the men had been offered seats on another flight.