The plane apparently had missed on its first approach to Nashville's airport and crashed on its second approach, hitting some trees before slamming into the ground shortly before 5 p.m.
District Fire Chief George Hickey said a witness saw the plane bank hard to the right and then go straight into the ground, missing several buildings.
"We'll wait until the experts get here. I'm no expert, but that tells me the pilot did one hell of a job," Hickey said.
Metro Police spokesman Don Aaron said three bodies had been recovered and rescuers were confident a fourth body was in the wreckage of the Gulfstream 690C, which was spread up to 300 feet, the (Nashville) Tennessean reported. The victims had not been identified.
Federal Aviation Administration spokeswoman Kathleen Bergen said the plane left Grand Bend Municipal Airport in Kansas en route to John C. Tune Airport in Nashville but crashed 10 miles south of its destination, the newspaper said.
The plane was registered to a Kansas company, Bergen said, declining to identify the company.
Witness Paula Tipps said she heard the plane's engine sputtering before it circled once and nose dived, causing an explosion and fire.
The Bellevue YMCA was evacuated as a precaution.
Chastity Mitchell of Bellevue was at the YMCA with her sons near where the plane crashed.
"I was with the kids. They were swimming. I was down on the benches watching them swim," Mitchell said. "I just heard a really horrible explosion and looked up [at the glass windows] and saw a wall of fire.
"I just started screaming for the kids to get out of the pool. Of course at that point the fire alarms weren't even going off. Very shortly after that they were.
"So we just jumped out of the pool and took off running."