In their nearly two-hour-long talks, Modi and Rouhani also held extensive deliberations on pressing regional and global issues such as ways to combat terrorism.
The two sides signalled a convergence of strategic interests in the region, including in war-torn Afghanistan.
On whether the kidnapping of Kulbhushan Jadhav, currently on a death row in Pakistan, from Iran was raised in the talks, officials in the Ministry of External Affairs (MEA) said the issue did not figure in the deliberations.
Apart from inking of lease contract between Iran's Port and Maritime Organization and India's Ports Global Limited (IPGL) to take over operation of existing facilities at the Shahid Beheshti Port -- Phase 1 of Chabahar -- for 18 months, the two sides signed avoidance of double taxation and the prevention of fiscal evasion with respect to taxes on income.
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In addition to the nine pacts, four more pacts were inked on the sidelines of Rouhani's three-day visit, officials said.
Talking about ramping up trade, the two leaders emphasised on the need to put in place an effective banking channel for business transactions.
"It was noted that permission for the Iranian Pasargadbank to open a branch in India was under advance consideration," a joint statement said.
It was also agreed to set up a joint committee of officials to examine feasible options, including Rupee-Rial arrangement and Asian clearing union mechanism to establish functional payment channels, the statement said.
At a joint press event with Rouhani, Modi said India is commited to deepen ties with Tehran, particularly in trade and investment and will support the construction of the Chabahar-Zahedan rail link to improve regional connectivity.
Modi said the two countries want a terror-free world and they were committed to stopping the expansion of those powers which encourage terrorism, extremism, drug trafficking, cyber crimes and other international crimes.
On his part, Rouhani said,"We are determined to combat terrorism and extremism."
Trying to reflect on growing congruence in bilateral ties, Rouhani said the two sides deliberated on a range of pressing bilateral, regional and international issues but did not disagree on even a "single topic".
Calling for an immediate end to all support and sanctuaries enjoyed by terrorist groups and individuals, the two leaders said states that aid, abet and directly or indirectly support terrorism should be condemned, according to the statement.
Recognising the challenges of terrorism and ideologies of violent extremism, the two leaders reiterated their strong commitment to combat terrorism in all its forms and manifestations.
"They called on the international community to end selective or partial approaches to combating terrorism and, in this regard, stressed the need to make every effort to reach an agreement on and conclude a comprehensive convention on international terrorism at the UN General Assembly," the joint statement said.
On Afghanistan, both sides stressed that the interests of peace and stability in the region are best served by a strong, united, prosperous, pluralisitic, democratic and independent Afghanistan and supported the National Unity Government in the country.
"They stressed the significance of strengthening India-Iran-Afghanistan trilateral consultations and coordination, including by suitably supplementing their cooperation on Chabahar.
The two leaders also reaffirmed their commitment to supporting the Intergovernmental Negotiations (IGN) for comprehensive reform of the UN Security Council.
They also underscored the need for strengthening and reform of multilateral financial institutions and enhancing the voice and participation of developing countries in international economic decision-making.
The two sides also agreed to enhancing cooperation in the maritime domain.
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