Kirkpatrick said the man was “hell-bent on creating the carnage and the damage that he did”.
The attack took place in New Orleans’ French Quarter – a bustling nightspot popular with locals and tourists.
Whit Davis, from Shreveport, Louisiana, was in a bar with friends when “people started running and getting under tables like it was an active shooter drill”.
“Everyone was just completely in shock,” he added.
“I visit New Orleans frequently and have never seen anything close to this bad.”
Jim and Nicole Mowrer, who were visiting New Orleans from Iowa, told CBS News, the BBC’s US news partner, that they witnessed the truck drive through a barricade at speed then heard gunshots and crashing noises.
They tried to help people they thought were wounded but realised the victims had died.
A hotel worker told CBS he had been closing down for the evening when he looked out the window and noticed “there was a lot of bodies lying on the ground”.
“The truck was speeding away. I immediately ran downstairs to see if there were some people I can help out and unfortunately some people did perish during that event.”
“The scene was just horrific,” he added.
FBI Special Agent Althea Duncan, who is leading the investigation, said an improvised explosive device was also found at the scene and they were working on confirming whether it was “viable”.
The suspect was wearing body armour at the time of the attack and a long gun was recovered from the scene, CBS reported, citing sources familiar with the investigation.
Law enforcement officials later told CBS that they are investigating whether the suspect was connected to or inspired by a foreign terror organisation.
They said they are exploring whether a black flag which appeared to be attached to the rear bumper of the pick-up truck during the attack could be an Islamic State (IS) group flag – or potentially tied to another foreign terror organisation.
US President Joe Biden told journalists his reaction is one of “anger and frustration”.
The White House said Mr Biden had called the city’s mayor this morning to offer “full federal support”.
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