The "man overboard" crisis arose on the Pakistan navy vessel (PNS-Nasr) at anchor in Darwin Harbour about 4.30am yesterday.
Superintendent Rob Burgoyne said he was taking part in the Australian Navy's Exercise KAKADU, disappeared into scrub and "didn't want to be found".
"We don't know what he's wearing but he's not in navy uniform and is small in stature," he said.
Water Police and a HMAS Newcastle helicopter began a sea search operation and his plastic-wrapped backpack was found floating in the water near Talc Head, on the Cox Peninsula, after he vanished, The Daily Telegraph reported.
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Humpty Doo cops, seven Territory Response Group members and a dog are among a dozen land searchers, the report said.
Burgoyne said the dog followed small foot prints about 6km south of Talc Head but the track went cold.
Police also found a pair of sandals or thongs believed to have belonged to the sailor, and are investigating whether residents at Belyuen, about 115km from Darwin, have seen anything suspicious.
KAKADU is Australian navy's largest maritime exercise with eight warships from Australia, Japan, the Philippines and Pakistan, 26 aircraft and 1200 people from 25 nations conducting simulated high-end warfare.