In a statement published Wednesday night, the Indonesian Ministry of Defence said the KRI Nanggala-402, a German-made submarine, lost contact during a torpedo drill in the Bali Strait -- a stretch of water between the islands of Java and Bali that connects to the Indian Ocean and Bali Sea.
The submarine asked for permission to dive, or submerge, at 3 a.m. local time (3 p.m. ET) before losing contact, it said. The statement added that an oil spill was seen in aerial surveillance near the dive point, around 7 a.m. local time.
The oil spill is "highly suspected" to have come from the vessel, Indonesian Navy spokesman First Adm. Julius Widjojono said.
"That oil spill location is the last time we had contact with the submarine," he said.
Widjojono said the submarine has the capability to dive up to 500 meters below sea level, but authorities estimate it went 100-200 meters below that depth.
He said authorities are holding out hope the crew are safe, but acknowledged the situation could be fatal at that depth.
"Let's pray for them so they can survive," he told local media Wednesday.
Several countries, including Australia, India and Singapore have offered to provide assistance.
Earlier on Wednesday, military chief Hadi Tjahjanto told Reuters that they were "searching in the waters of Bali, 60 miles (96 km) from Bali, (for) 53 people."
Indonesia is deploying four warships to search for the submarine, including a Rigel warship equipped with sophisticated sonar that can precisely detect the vessel's position, Widjojono said. That ship is currently en route from Jakarta.
Two ships equipped with side-scan sonar, a tool used for mapping the seafloor, began searching the area Wednesday, the Ministry of Defence said. The International Submarine Escape and Rescue Liaison Office (ISMERLO), an organisation that facilitates an international response for distressed submarines, is also providing assistance, the ministry said.
The 1,395-ton KRI Nanggala-402 was built in 1977 by the German shipbuilding company Howaldtswerke-Deutsche Werft (HDW) and joined the ranks of the Indonesian Navy in 1981, according to the Ministry of Defence statement.
The submarine underwent a two-year refit in South Korea that was completed in 2012, according to the Indonesian cabinet secretariat's website.
Indonesia in the past operated a fleet of 12 submarines purchased from the Soviet Union to patrol the waters of its sprawling archipelago.
But now it has a fleet of only five, including two German-built Type 209 submarines and three newer South Korean vessels.
Indonesia has been seeking to upgrade its defence capabilities, but some of its equipment still in service is old and there have been deadly accidents in recent years, in particular involving ageing military transport planes.