He said the fire was punctuated by the pops of small explosions.
Fisher also urged people to stay away from debris, as some could be risky to bystanders.
It plunged into a field at approximately 4 p.m. CDT (5 p.m. EST) on Monday in Mississippi's LeFlore County, about 100 miles (160 km) north of Jackson, the state capital. He and Fisher said some debris could be unsafe to bystanders.
The cause of the crash was not immediately known and the identities of those killed were not immediately released.
The plane belonged to Marine Aerial Refueler Transport Squadron 452 (VMGR-452) based at Stewart Air National Guard Base in Newburgh, New York, the New York Air National Guard said.
Of the deceased, 15 were Marines and one was a sailor, according to Richard Spencer, the Trump administration's nominee for Navy secretary, who addressed the subject during the opening remarks of his Senate confirmation hearing this morning.
Greenwood Fire Department Chief Marcus Banks told the Greenwood Commonwealth newspaper that firefighters were driven back by several "high-intensity explosions" that may have been caused by ammunition igniting.
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The plane crashed off Mississippi County Road 547, near USA 82, on a stretch of fields near the Sunflower-Leflore county line, about 85 miles north of Jackson, said Greg Flynn, a spokesman for the Mississippi Emergency Management Agency.
The KC-130 first appeared in 1962 with a range of about 1,500 miles as a tanker and more than 3,000 miles as a cargo transport.
Mississippi Governor Phil Bryant said the incident was a "tragedy".
Debris was scattered for miles across the flat countryside Tuesday. Other potential victims were still being sought Monday night, the paper said. James said the flight was carrying a team from the Marine Base at Camp Lejeune, North Carolina.
They were headed to Yuma, Arizona for pre-deployment training.
Snowden lived in NY, where his Marine unit was based. The names of those killed were being withheld until their families could be notified.