"A T-4 training aircraft that belongs to the Air Self-Defense Force crashed at 3:08 pm (0608 GMT) after radar lost (it) near a lake... after taking off at Komaki Air Base" in central Japan, Defence Minister Gen Nakatani told reporters.

Nakatani said two people were on board, without revealing their identity.

"We don't know what caused the aircraft to crash, but we will continue to do our utmost to save lives," he said, adding that the military has been carrying out search operations.

An aircraft part was found near the scene, but it was unclear whether it was from the crashed plane, Nakatani said.

The T-4 seats two and is a "domestically produced, highly reliable and maintainable training aircraft... used for all basic flight courses", according to the defence ministry website.

The aircraft was flying around Lake Iruka near Inuyama city north of Nagoya.

"There is no sight of the plane yet. We've been told that an aerial survey by an Aichi region helicopter found a spot where oil was floating on the surface of the lake," local fire department official Hajime Nakamura told AFP.

Aerial footage of the lake broadcast by NHK showed an oil sheen on its surface, dotted with what appeared to be various pieces of debris.

Jiji Press said the local municipality had said there had been no damage to houses in the area.