The first three shipments of Indian wheat to Afghanistan were unloaded in the morning, according to the Iranian ports organisation.
Swaraj met her Iranian counterpart Javed Zarif held a meeting on Saturday in Tehran and discussed about the Chabahar port project among other issues.
The Chabahar port in Iran, which gives India access to central Asia bypassing Pakistan's Gwadar Port, which is being built by China, was inaugurated on December 3.
The port in Iran's Sistan-Balochistan province on the energy-rich nation's southern coast is easily accessible from India's western coast and is increasingly seen as a counter to Pakistan's Gwadar port, which is being developed with Chinese investment and is located around 80 kms from Chabahar.
The inking of the port deal had caused tensions between Tehran and Islamabad at the time.
The nation anticipates that it will become a key transit route to land-locked Afghanistan and Central Asia and enable more Indian commodities to be exported to Russian Federation.
India, Afghanistan and Iran have been working together and constantly to create an alternate and reliable trade access bypassing Pakistan.
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Chabahar provides India with an easy land-sea linkup with Afghanistan.
Rouhani, however, downplayed the Pakistan angle in his inauguration speech and said the port will bring "more engagement and unity" among regional countries. India's commitment for the port is $500 million.
In the first phase of the port of Shahid Beheshti, 15 million cubic meters of dredging, 203 hectares of new land, and 1,650 breakwaters have been constructed, and its basin depth is 16.5 square meters.
Minister of Roads and Urban Development Abbas Akhoundi said investments worth 40 trillion rials ($1 billion) are needed to connect Chabahar to Iran's national railroad.
"The ministers agreed that an integrated development of connectivity infrastructure including ports, road and rail networks would open up greater opportunities for regional market access and contribute towards the economic integration and benefit of the three countries and the region", the statement said.
Iranian President Hassan Rouhani, center, speaks during the inauguration a newly built extension of the port of Chabahar, near the Pakistani border, on the Gulf of Oman, southeastern Iran, Sunday, Dec. 3, 2017. As per the reports, the Chabahar port pact allows the Afghanistan to import and export goods from markets like India after reducing its dependence on Pakistan's Karachi port.
Over a month ago, India had sent its first consignment of wheat to Afghanistan by sea through the Chabahar port, marking opening of the new strategic transit route.