"There are no survivors," Correa wrote on Twitter, several minutes after first posting news of the crash. "This is a tragedy."
He said the plane was carrying 19 paratroopers, two pilots and a mechanic.
The plane went down in the eastern province of Pastaza, near the border with Peru.
Defense Minister Ricardo Patino said he was on his way to the scene.
The army said the plane was carrying soldiers for a parachuting master class when it crashed.
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