The Brave Eagle went down after taking off from Chih Hang Air Base in southern Taitung county at 8:40 am (0040 GMT), the air force said in a statement.
The air force said the jet suffered “dual engine failure” but a special task force would investigate “to clarify the cause and ensure training safety”.
China claims Taiwan as part of its territory and has threatened to use force to bring it under its control.
The pilot of the aircraft that crashed Saturday had 183 flying hours, the air force said.
Taiwan's Mirage 2000 fighters were purchased in 1992 from France in an arms deal that angered China.
Taiwan's military is under pressure from China, which has in recent years ramped up incursions by fighter jets and warships around the island -- actions that military experts dub as grey-zone tactics that serve to exhaust the island's armed forces.
Speaking to reporters on Saturday, President Lai Ching-te said he hoped the opposition-controlled parliament would remedy the sections of the defence budget that have been frozen or cut to show “our full support for the military”.
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