The two leaders discussed issues of mutual and regional interests.
The meeting which comes amid escalating face-off between Iran and the United States on Tehran''s nuclear programme, took place days after PM Modi and US President Donald Trump displayed a new level of friendship at Howdy Modi event in Houston, and in their two other subsequent meets on UNGA sidelines.
"PM @narendramodi met with President of Iran @HassanRouhani at UNGA. Discussed bilateral cooperation and exchanged views on the situation in the region," Ministry of External Affairs Raveesh Kumar tweeted.
The two leaders could not hold a planned meeting on the sidelines of the Shanghai Cooperation Organisation (SCO) summit in Bishkek, Kyrgyzstan, in June due to scheduling issues.
India, the world''s third biggest oil consumer, meets more than 80 per cent of its oil needs through imports. Iran was its third largest supplier after Iraq and Saudi Arabia till recently.
The six-month-long exemptions from US sanctions to India and seven other countries to buy oil from Iran expired on May 2 as Washington did not extend it.
Indo-Iran ties have been on a upswing in the past few years.
Prime Minister Modi visited Tehran in May 2016 with an aim to craft a strategic relationship with Iran and expand India''s ties with the West Asia.
During the visit, India and Iran signed nearly a dozen agreements, centrepiece of which was a deal on development of the strategic Chabahar port.
Later, India, Iran and Afghanistan signed a trilateral agreement providing for transport of goods among the three countries through the port.
In February 2018, Rouhani visited India, becoming the first Iranian President to visit India in a decade. During his visit, the two sides signed a dozen agreements.
(With inputs from PTI)