When the TSA employee directed Almonte for a further screening, he apparently realized what was going on and ran.
Port Authority police reviewed surveillance video, which they said clearly shows Almonte running away from the terminal.
JetBlue cancelled eight flights and delayed six others while the incident was investigated.
Almonte later surrendered, accompanied by his lawyer.
Charges were pending and expected to be possession of a weapon and possession of stolen property.
Investigators believe Almonte did not realize he had the weapon in his luggage, and fled when he was confronted by the screener.
The incident is not believed to be terrorism related.