A total of eight passengers were removed.
“American Airlines singled us out for being black, embarrassed us, and humiliated us,” they said in a statement.
The three men – Alvin Jackson, Emmanuel Jean Joseph, and Xavier Veal – were eventually allowed to re-take their seats on their original flight.
In a letter to employees dated 18 June, Mr Isom said he was “incredibly disappointed by what happened on the flight and the breakdown of our procedures”.
“We fell short of our commitments and failed our customers,” he said.
He added that the airline is “steadfast in our commitment” to working with civil rights organisations such as the National Association for the Advancement of Colored People, or NAACP, to “rebuild trust”.
The incident is not the first time that American Airlines has faced allegations of discrimination.
In a separate incident in 2017, the NAACP warned black travellers to avoid the airline, citing a pattern of “disrespectful” and “discriminatory” behaviour as well as a “corporate culture of racial insensitivity and possible racial bias”.
They lifted the advisory the following year after the carrier announced it had made changes to its operations.
On 4 June this year, however, it warned that it could reinstate the warning unless American gave a “swift and decisive response” to the January incident.