While the new extension opens up a strategic transit route from India to Afghanistan and Central Asia - bypassing Pakistan - the Iranian government has reportedly asked India to "manage" or operate the first phase of the port, till the work for the second phase is finalized.
A day earlier, Indian External Affairs Minister Sushma Swaraj held a meeting with her Iranian counterpart, Javed Zarif, in Tehran to review the implementation of the Chabahar Port, India Times said.
Later, Radhakrishnan, along with ministers from Afghanistan and Iran, discussed issues related to the full operationalisation of the Chabahar port, a statement from India's foreign ministry said.
Iran's President Hassan Rouhani inaugurated the Shahid Beheshti Port's first phase in a ceremony that was attended by ministers, envoys and officials from 17 countries, including Minister of State for Shipping Pon Radhakrishnan.
Transport Minister Abbas Akhoundi said Chabahar on the Gulf of Oman will "soon become an important commercial hub for Iran". It involved several subcontractors, including a state-run Indian company, and brings the capacity of the port to 8.5 million tonnes of cargo annually, from the previous 2.5 million tonnes.
Chabahar is Iran's only oceanic port town and consists of two separate ports named Shahid Kalantari and Shahid Beheshti.
Chabahar provides India with an easier land-sea route to Afghanistan.
Referring to the Indian shipment in October, it said, "The three sides also commended the recent joint efforts, which led to the transit of first tranche of 110,000 tonnes of wheat from India to Afghanistan through the Chabahar port".
The document was signed at the presence of Iranian President Hassan Rouhani, Indian Prime Minister Narendra Modi, and Afghan President Ashraf Ghani.
"We should go after positive competition", he said in his inauguration speech.
Rouhani added that the port is also politically important "because it will connect us to the eastern and northern countries, and even to European countries in the future, and this is politically important to us".
Further boosting up the bilateral ties between India and Iran, Swaraj, on her way back from Sochi in Russian Federation, made an unannounced visit to Tehran, ahead of the inauguration of the first phase of the key port - in which the Iranian government has invested about one billion dollar.
A railway route is also under construction from Chabahar to Zahedan (centre city of Sistan-Baluchestan Province) to boost the capacity of the new strategic transit route.