A suicide attacker also detonated a car bomb near a U.S.-led coalition convoy, wounding a coalition soldier.
The International Security Assistance Force said the plane had reported a technical problem before going down and hostile fire did not appear to be the cause. The British Ministry of Defense said the dead included 12 Royal Air Force personnel, a Royal Marine and an army soldier.
The "aircraft was supporting a NATO mission. It went off the radar and crashed in an open area in Kandahar," said Maj. Scott Lundy, spokesman for the International Security Assistance Force.
The crash happened about 12 miles west of the city of Kandahar, he said.
Lundy gave no other details, but ISAF said in a statement that the plane had announced it had a technical problem before going down.
However, shortly after the crash, a purported spokesman for the Taliban, Abdul Khaliq, claimed responsibility.
"We used a stringer missile to shoot down the aircraft," he said.
Haji Eisamuddin, a local tribal elder, told The Associated Press by phone that the wreckage of the plane was burning in an open field, and that coalition forces had started arriving at the scene.
"I can see three-four helicopters in the sky, and coalition forces are also arriving in the area," he said.
The plane crash and the violence came amid the deadliest upsurge in militant attacks and fighting in Afghanistan since the ouster of the Taliban regime by U.S.-led forces nearly five years ago.
In the deadliest incident, insurgents attacked a police checkpoint on Friday, killing five policemen and wounding seven others in the Grieshk district of Helmand province, about 250 miles southwest of Kabul, said Ghulam Muhiddin, the Helmand governor's spokesman. Police returned fire and killed three Taliban and wounded two.
Muhiddin said the Taliban abducted four other police, and hundreds of police were hunting for them Saturday.