The Hawk 108 fighter jet took off at 11am and contact was lost at 11.30am when the plane was believed to be near the border of the Malaysian states of Pahang and Terengganu.
The two airmen's bodies were found in a swampy area in Chukai, a town in Terengganu, the spokesperson who did not want to be named, told AFP.
"The plane has not been found yet and we are investigating," the spokesperson said without providing more details.
There have been other recent cases of military plane incidents in Malaysia.
In December, a military Beechcraft B200T turboprop crashed in the town of Butterworth in northern Malaysia.
In May last year, an air force Aermacchi MB339CM jet crashed in a small town in the rural state of Pahang but there were no casualties.
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