Another 13 people were injured in the incident at the Los Llanos base, which sent flames and a plume of black smoke billowing into the air, the ministry said in a statement. Seven were in serious condition, one person was treated and released from hospital, while the conditions of the five others were not disclosed.
Most victims were not believed to be Spaniards but military personnel from other NATO member countries participating in the program, according to a Defense Ministry official who spoke on condition of anonymity because of ministry rules preventing him from being named.
Based on initial reports, there were no US personnel killed but an unknown number were treated for minor injuries, said Air Force Lt. Col. Vanessa Hillman, a Pentagon spokeswoman.
Nine of the injured were Italians taking part in the training course, the Italian defense ministry said in a statement. Seven suffered slight injuries but the conditions of two were still being assessed at a hospital.
The two-seat jet was taking off but lost thrust and crashed into an area of the base where other aircraft involved in the NATO exercise were parked, the Spanish Defense Ministry said. The Italian statement said "numerous" helicopters were damaged.
NATO Secretary General Jens Stoltenberg said he was "deeply saddened by the crash of a Greek fighter jet at the Los Llanos base in Spain, which has caused many casualties."
He did not specify their nationalities in a statement, but called the crash "a tragedy that affects the whole NATO family."
The Spanish ministry said the jet that crashed was taking part in a NATO training exercise called the Tactical Leadership Program.
According to a US Air Force Website, TLP was formed in 1978 by NATO's Central Region air forces to advance their tactical capabilities and produce tactics, techniques and procedures that improve multi-national tactical air operations.
The first TLP course took place at Fuerstenfeldbruck Air Base, Germany. It has been held at the Spanish base since June 2009.
The Los Llanos base is near the southeastern Spanish city of Albacete, about a two and a half hour drive from Madrid.