The sources say that more Navy officers in the Western Command are likely to resign over the incident, the cause of which is not known.
The submarine docked at the Mumbai harbour early on Thursday. Three of its compartments were found locked from inside. Naval sources said the two missing personnel could be inside any of these. The search operations are likely to resume soon.
"I am very sad about the developments. After the Sindhuratna incident, the Navy chief came to me. He was very upset and asked me to accept his resignation immediately," Defence Minister AK Antony said. "I consulted the Prime Minister on his resignation. He (Admiral Joshi) is a fine admiral and a very fine human being," Antony added.
According to the Navy, its crew members on board the submarine Sindhuratna detected smoke coming out from a chamber during a routine exercise early on Wednesday. Seven crew members were airlifted to a naval hospital after they inhaled smoke. The Navy was able to bring the smoke under control in 24 hours.
INS Sindhuratna is a Kilo-class vessel and was 100 nautical miles off the Mumbai coast when the incident happened.
Two navy personnel are still recorded as "unaccounted for". The search for them continues.