Terrell Suggs Allegedly Brandished Gun, Threatened To Kill Man During Starbucks Tiff

10:23 AM PT -- Suggs, through EAG Sports rep Denise White, issued a statement on the incident to TMZ Sports ... and Terrell says he was in fear for his safety.

"I was in a quiet area of Scottsdale in the middle of the day in a Starbucks drive-thru near my home when an incident happened with a vehicle behind me. I was getting coffee, I was not looking for any trouble," TS said.

"When the man in the other vehicle escalated the situation, I feared for my safety not knowing what his intentions were. Throughout the incident, I was the one who felt in danger, while fearing I would be followed home and for the safety of my family nearby at my residence."

TMZ Sports has learned Terrell Suggs' arrest on Tuesday stemmed from a March incident in which he allegedly brandished a gun and threatened to kill a man during an argument at a Scottsdale, Arizona Starbucks.

According to court documents we obtained, the altercation happened at a drive-through at the coffee joint at around 12:28 PM on March 10.

In the docs, officials say Suggs had driven past the ordering speaker ... and when he put his Range Rover in reverse to remedy the situation, he made contact with another man's vehicle.

Although there was apparently no damage to the car, cops say both drivers exited their vehicles and an argument ensued, but the two eventually returned to their rides and made their orders.

However, as Suggs was about to leave the area ... he allegedly flipped off the man -- which authorities say kicked off another verbal argument.

According to the docs, the man swore at Suggs, before the ex-NFL superstar challenged him to a fight. The former Baltimore Ravens pass rusher allegedly then called the man a "p***y ass cracker," before adding, "I'll kill your bitch ass."

As Suggs then pulled out to leave, officials say he flashed a black handgun in his left hand outside of his driver's side window.

"The handgun was never pointed at the victim," officials wrote in the docs, "and was just merely shown."

Still, authorities say the man believed Suggs -- who was not accused of ever getting physical with the alleged victim -- was threatening him with it.

The man reported the incident to police a short time later ... and according to authorities, the entire incident was captured on a dashcam recorder.

About a month later, at 2:40 PM on Tuesday, cops say they pulled over Suggs ... and arrested him for his alleged role in the encounter.

Suggs was ultimately booked on two charges -- one felony count of disorderly conduct involving weapons, and one misdemeanor count of threatening or intimidating. He appeared before a judge on Tuesday evening, and after a quick hearing, he was released.