Terence Crawford Held By Cop at Gunpoint, on Video

4:13 PM PT -- Omaha's Mayor John Ewing just released a full statement ... acknowledging he's aware of the incident -- and, he's promised to ensure the impending internal investigation will be thorough and transparent.

Mayor Ewing is asking members of the community to try to remember the triumphant spectacle of the parade yesterday instead of focusing simply on the unforutnate circumstances surrounding how it ended ... and, he says he's committed to make every resident feel safe in Omaha.

Terence Crawford was forced out of a car at gunpoint by a police officer with the tense exchange caught on video ... and, it's leading to an internal investigation.

Video is circulating online showing the boxer slowly unbuckling his seatbelt, opening his door and stepping out of the car ... while an officer at his window holds a flashlight in one hand and a gun in the other.

The officer repeatedly tells Crawford to step out ... and, he replies at one point, "I ain't reaching for no gun" -- with his hands up the whole time.

Crawford was then patted down by the officer before the clip comes to an end.

The Omaha Police Department released a statement Sunday morning ... explaining the city's mayor and chief of police are ordering a review of the traffic stop by the internal affairs department.

The statement reads, "Shortly before 1:30 a.m., officers working in the downtown area observed a vehicle driving recklessly near North 12th and Capitol Avenue. A traffic stop was conducted at Cass Street."

It continues, "While speaking with the driver, an officer observed a firearm on the driver’s side floorboard. For safety, all four occupants were ordered out of the vehicle at gunpoint."

Ultimately, cops learned everyone in the vehicle was licensed to carry ... and a police supervisor and lieutenant responded to the scene when requested by Crawford.

Ironically, Bud received a hero's welcome in Omaha earlier Saturday ... appearing as the man of the hour at a parade celebrating his recent upset win over Canelo Alvarez. Clearly, the day didn't end the way anyone thought it would.

Terence is an undefeated boxing champ -- he holds a 42-0 across his illustrious career -- who is currently the undisputed welterweight and super middleweight champion.