The offer was made by visiting Indian Navy chief Admiral D K Joshi when he called on President Mahinda Rajapaksa.
Joshi is in Sri Lanka to attend the international naval maritime conference held in the southern port town of Galle.
The Indian Navy will offer training to Sri Lankan naval officers to follow the four-year Bachelor of Technology course that is currently restricted to Indian officials, a presidential release said.
The Sri Lankan Navy would be afforded priority though there was a great demand for this course from many countries.
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Among the other topics discussed was the problem of combating piracy in the Indian Ocean towards which "the Sri Lanka Navy has made a big contribution", Joshi said.
He said that although incidents of piracy have seen a decline in recent years, Sri Lanka and India must continue to be vigilant.
Joshi travelled to several major maritime locations around Sri Lanka including Trincomalee, Mannar, the Jaffna Peninsula, Galle and Hambantota.