"Unfortunately the two pilots are dead," one of the officials said, adding that the Phantom crashed about 2km outside the airport and there were no reports of injuries to any bystanders or residents in the wider area.
Footage from public broadcaster ERT showed the F-4 performing a right turn a few metres above the ground seconds before it crashed and erupted into a fireball.
Eleven water-dropping planes and helicopters assisted 85 firefighters in an effort to contain a fire following the crash, which remained at some distance from the viewing area at Athens Flying Week, an annual air show.
"We were all stunned. It hadn't been airborne for more than three minutes," an eyewitness told ERT.
Air force officials said the bodies of the two pilots were located during the rescue operation.
Loudspeakers at the air base urged people to leave the area, according to ERT.
The Tanagra air force base is 60km north of Athens.
Organisers cancelled remaining events planned over the weekend, while the fire prompted an evacuation order in an area near the base.
Cyprus' Defence Minister Vasilis Palmas said that he had called his Greek counterpart Nikos Dendias to express the condolences of his government.
"It is with deep sadness that I learned of the death of the two officers of the Hellenic Air Force, who lost their lives in the tragic accident that occurred during the air show at Tanagra Air Base," Palmas wrote in an online post.
with AP
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