Defence analysts have warned that the vessel could have already broken into pieces if it has sunk to depths believed to be as much as 700 metres. That is well below what it was built to withstand.
Indonesia's president Joko Widodo asked his country to pray for the crew, while Australian Defence Minister Peter Dutton said initial reports raised the prospect of a "terrible tragedy".
The German-built submarine was scheduled to conduct live torpedo exercises when it asked for permission to dive. It lost contact shortly afterwards.
Search teams were focused on an area around the oil slick.
The exact location of the vessel had yet to be pinpointed, the navy said, with warships and helicopters assisting in the hunt.
Race against time
Damage to the submarine's fuel tank could spell big trouble.
"If your tank's cracked it is not very good news," said Collin Koh, a naval affairs specialist and research fellow at the S Rajaratnam School of International Studies in Singapore.
"Because we are talking about the pressure hull of the submarine being breached. So it could cause potential flooding."
Neighbouring Singapore and Malaysia have already dispatched ships that are expected to arrive in the coming days, including the city-state's MV Swift Rescue — a submarine rescue vessel.
India said Thursday it had sent a ship to assist in the hunt, while the United States, Australia, France and Germany are among other nations that have offered help.
Indonesia's military has so far refused to comment about whether the decades-old submarine, carrying 53 crew, was over capacity.
But it has said the submarine might have sunk to vast depths after a blackout that left its crew powerless to control the vessel.
"There are too many unknowns right now," said Curie Maharani, a defence expert at Indonesia's Bina Nusantara university.
"But what we do know is that it's a race against time." Frank Owen, secretary of the Submarine Institute of Australia, warned that rescuing any surviving crew quickly would be near impossible.
"If the submarine is on the seabed, and if it is in the depth of water that is there, there is little they can do to actually get the people out," he told Australian media.
Workhorse submarine
Indonesia, which has been moving to upgrade its ageing military equipment in recent years, has five German and South Korean-built submarines in its fleet.
The 1300-tonne KRI Nanggala 402 was first delivered for service in 1981. It is a Type 209 diesel-electric attack submarine, a model that over the past half century has featured in more than a dozen navies around the world, including those of Greece, India, Argentina and Turkey.
While Indonesia has not previously suffered a major submarine disaster, other countries have been struck by accidents in the past.
Among them was the 2000 sinking of the Kursk, the pride of Russia's Northern Fleet.
That submarine was on manoeuvres in the Barents Sea when it sank with the loss of all 118 aboard.
An inquiry found a torpedo had exploded, detonating all the others.
Most of its crew died instantly but some survived for several days — with a few keeping heartbreaking diaries written in blood to their loved ones — before suffocating.
In 2003, 70 Chinese naval officers and crew were killed, apparently suffocated, in an accident on a Ming-class submarine during exercises in 2003.
Five years later, 20 people were killed by poisonous gas when a fire extinguishing system was accidentally activated on a Russian submarine being tested in the Sea of Japan.
And in 2018, authorities found the wreckage of an Argentine submarine that had gone missing a year earlier with 44 sailors aboard.