A consent order released by the Transportation Department on Friday says Delta violated the law "when it removed and denied re-boarding" to the Muslim passengers.
The order also requires Delta to provide cultural-sensitivity training to all cabin crew members and customer service staff involved in both cases.
The airline for its part said it could have handled both incidents better but disagreed that its conduct was discriminatory.
The first incident occurred on July 26, 2016, when a Muslim married couple boarded a flight in Paris, France to return to their home in Cincinnati, Ohio. The wife "was wearing a head scarf" at the time.
A fellow passenger told a flight attendant the couple made her “very uncomfortable and nervous” because she saw the husband insert "something plastic into his watch" and do "something with it." The passenger described the couple, who are U.S. citizens, as “fidgety, nervous, and sweating,” according to the consent order.
Flight attendants also told the plane's captain they saw the husband "texting on his cell phone using the word 'Allah' several times" and raised concerns over him not smiling after their making eye contact with him. The captain then asked security officers to remove the passengers from the plane for additional vetting, the Transportation Department said.
The captain later refused to let the couple re-board the plane, after they were interviewed and cleared, because the flight attendants were "uncomfortable" having the couple on the flight, the order said.
If it weren't for the couple's "perceived religion, Delta would not have removed or denied them re-boarding," the order said.
The second incident occurred five days later on July 31, 2016, when a Muslim man boarded a flight from Amsterdam, Netherlands, to New York City.
Passengers at the departing gate told Delta’s flight crew they observed the man making “significant eye contact” and later speaking with a person of similar ethnicity in the gate area. The person he spoke to didn't board the plane and appeared to have given him a small package, according to the Transportation Department's investigation.
At the captain's request the flight's First Officer walked through the cabin but "observed nothing remarkable" about the passenger. Delta Corporate Security also informed the captain that the man's record showed “no red flags.”
The captain proceeded to begin departure but later "returned to the gate" because "the flight attendants expressed, without any intervening incident, that they remained uncomfortable," according to the order.
The Transportation Department found the man was not subjected to additional security screening prior to being relocated on another flight, leading the agency to conclude that his removal "was discriminatory."
Delta disagrees with the federal department's characterization of their actions as "discriminatory."
The airline told NBC News in a statement that its "best customer service was not reflected" in how the incidents were handled, but "we disagree with the Department of Transportation's contention that Delta engaged in discriminatory conduct."
Delta said it has "worked to improve our investigative process since these incidents and we have supporting programs, policies, training and procedures that back up our commitments in this area.”
The company also said in a statement in the consent order, that it is "a global airline that serves customers of all races, ethnicities, and religious affiliations ... Delta stands by its record as an airline where all are welcome, and unlawful discrimination of any kind is not tolerated."