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The submarine failed to report back with results of a training exercise while in waters in North Bali on Wednesday.
Navy spokesman First Admiral Julius Widjojono said it had been taking part in a torpedo drill, but failed to relay results from the exercise as expected.
The KRI Nanggala 402 submarine was built in Germany in 1981, and the 60m vessel has a cruising speed of 21.5 knots.
Military chief Hadi Tjahjanto confirmed to Reuters that a total of 53 people are missing.
"We are still searching in the waters of Bali, 60 miles (96 km) from Bali, (for) 53 people," he said.
Tjahjanto said that assistance in the search for the submarine and missing crew members had been sought from Australia and Singapore.
He added that contact with the vessel was lost at 4.30am on Wednesday.
Military information group Janes reports that the navy sent a distress call to the International Submarine Escape and Rescue Liaison Office (ISMERLO) shortly before 9.40am, reporting the vessel missing.
It added that the navy has dispatched 'several' ships to the area to search for the Nanggala, which is thought to have disappeared around 26.5 miles northwest off Singaraja in Bali.
"The TNI-AL has dispatched several warships to the area, including the hydrographic ship, KRI Rigel (933), for the search," the report from Janes said.
"Other vessels currently on the scene include the TNI-AL's first-of-class Fatahillah corvette (361), the lead Bung Tomo-class corvette (357), and the Kapitan Pattimura (Parchim I) class corvette, Teuku Umar (385)."
According to the Indonesian cabinet secretariat's website, the 1,395-tonne vessel was built in Germany in 1978, and underwent a two-year refit in South Korea, which was completed in 2012.
Reuters reports that in the past, Indonesia operated a fleet of 12 submarines - which had been purchased from the Soviet Union - to patrol its waters.
However, it now has just five, including two German-built Type 209 submarines and three newer South Korean vessels.
The news agency says Indonesia has been 'seeking to upgrade its defence capabilities', but some of its equipment currently in service is 'old' - and that in recent years there have been deadly accidents involving ageing military transport planes in particular.
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