Mr Sinha met the five Indians - Emerson, P. Augustus, R. Wilson, K. Prasath and J. Langlet - who were awarded the death sentence by the Colombo High Court Oct 30 on charges of drug trafficking.
The high commissioner met them at the superintendent's office where he handed over some clothes and toiletries and enquired about their welfare.
He assured them of unstinted support and cooperation of the Indian government in ensuring that their case receives the utmost attention, said official sources.
The fishermen appeared in good health and requested permission to write to their relatives in Tamil Nadu and also to make telephone calls.
The prison authorities readily agreed and said they would arrange for telephone calls to be made by the prisoners in a couple of days.
Meanwhile, they were free to write letters to their relatives, the sources added.
The fishermen expressed happiness at the high commissioner personally coming to meet them and thanked him for this gesture.
India has conveyed to Sri Lanka its concern over the death sentence and is waiting for the final copy of the court judgment in order to appeal against it.
India's external affairs ministry spokesperson Syed Akbaruddin said earlier in New Delhi that India and Sri Lanka have in place a "legal architecture" to deal with such cases and cited an earlier instance in which the death sentences of two Indian nationals were commuted to life imprisonment by the then Sri Lankan president.
The two Indians served some period of their sentence in Sri Lanka, and under an agreement by which a sentenced prisoner can serve the sentence in their respective countries, the two were transferred to India in 2013. While one has completed his sentence and been set free, the other is still serving his sentence in India, he said.