According to a coastguard statement, preliminary investigations found the men had left Bangladesh bound for either Thailand or Malaysia in six motorised boats about 45 days ago.
At some point on their journey, the men are said to have changed vessels.
"It's possible that most of these people are still alive," said Satya Prakash Mishra, commander of the Andamans region coast guard.
According to one survivor, identified as Mohammad Ismail Arafat, there had been 412 men, aged between 18 and 60 on the boat, which had little food or water and only a plastic sheet for a sail.
He also said he and others had paid a Bangladeshi agent for promised jobs in Malaysia.
"We were left to the mercy of God ... after drifting for 10-15 days when finally we saw a lighthouse, many jumped into the water," a coastguard statement quoted him as saying.
The Andaman and Nicobar islands lie about 1,200km off India's east coast. It comprises a chain of 536 islands in the Bay of Bengal of which only 58 are inhabited.