The collision between the fighter jet and a Cessna C-150 occurred at around 11 a.m. near Moncks Corner, north of Charleston, the Federal Aviation Administration said in a statement.
The two people aboard the Cessna were both killed, a spokesman for the National Transportation Safety Board said. The agency is investigating the crash.
Authorities are still searching for their bodies, and have not released their identities, Bill Salisbury, the Berkeley County coroner, told a news conference.
The small plane carrying the local residents had left the Berkeley County airport a few minutes before the crash and was probably going to Myrtle Beach, South Carolina, Salisbury said.
The pilot of the military aircraft, identified as Major Aaron Johnson, ejected safely and was taken for a health evaluation, according to a statement from Shaw Air Force Base in South Carolina, where the F-16 was based.
Johnson is expected to make a speedy return to the base and could resume flying next week, Colonel Stephen F. Jost said at a news conference on Tuesday.
Authorities have located the military plane and parts of the Cessna, Salisbury said.
"Our thoughts are with the friends and family of anyone aboard the civilian aircraft," Shaw Air Force Base said in a statement posted on Twitter.
"From what I understand from a witness, the military plane struck the other, small aircraft broadside," Salisbury said.
Debris from the small plane had been found scattered over a wide area, including in a rice field, local authorities said. There were no reports of injuries from any debris.
At least 20 agencies were involved in the response.
Johnson was flying a routine training mission from the air base to Charleston and back, Jost said.
"Our pilots are well-trained to fly the approaches in and out of there, and all of the facts at this point indicate that the pilot was talking to air traffic control as they normally do when the accident occurred," Jost said. "Everything beyond that is subject to speculation."
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