The premier had added that prior to arriving in NY he had visited Saudi Arabia and spoken to Saudi Crown Prince Mohammed bin Salman who also asked him to talk to Rouhani. Washington had blamed Tehran for an attack on the world's biggest crude oil processing facility in Saudi Arabia.
Prime Minister Imran Khan also held a meeting with Chinese President Xi Jinping.
Tensions between Iran and the United States increased after the USA unilaterally withdrew from the 2015 Joint Comprehensive Plan of Action (JCPOA) in May 2018, reimposing sanctions against Tehran.
However, media reports, citing sources, had claimed that the goal of the visit was to mediate between the two countries, adding that the dates were yet to be finalised.
However it emerged earlier that PM Khan will visit Saudi Arabia on October 29 to participate in three-day Future Investment Initiative (FII) 2019 in Riyadh over the invitation of Saudi King Salman bin Abdulaziz Al Saud.
"Speaking to Majid al-Ali, editor of the Kuwaiti newspaper Al-Rai, and other Arab journalists, Mohammad Javad Zarif emphasised the importance of the "Hormuz Peace Endeavour (HOPE)" presented by President Rouhani in his address to the UN General Assembly". Before departing to NY.
The announcement of the possible visit comes after Khan last month described a request by U.S. President Donald Trump, asking the Pakistani leader to help defuse tensions with Iran.
Another official said Pakistan remained in contact with both Tehran and Riyadh to find a negotiated settlement of their current crises.
Pakistan enjoys close strategic ties with Saudi Arabia but at the same time consider Iran as an important neighbour.
Quoting Foreign Office sources, The Express Tribune reported that Khan is likely to visit Tehran and Riyadh later this month to mediate between Iran and Saudi.
Saudi Arabia has supported Washington's "maximum pressure" campaign against Iran after President Donald Trump previous year quit an worldwide nuclear pact and re-imposed sanctions, saying the deal was flawed as it does not curb Iran's ballistic missile program or its support for regional proxies.