The two leaders agreed that they and their officials will continuously remain in touch to ensure that the region remains stable, Foreign Secretary Vijay Gokhale said at a media briefing.
The Iran issue, along with 5G, trade and defence relations, was raised by Modi with Trump during their bilateral meeting on the sidelines of the G20 Summit here.
"So far as Iran was concerned, the Prime Minister outlined our energy concerns as well as our concerns regarding peace and stability in the region," the Foreign Secretary said.
"On Iran, the primary focus was how we ensure stability in that region. It is that instability affects us in many ways, not just in terms our energy needs but in terms of the very large diaspora that we have in the Gulf eight million Ind in the Gulf region and economic interests," he added.
He said it is in the interest of India and the US that the region remains stable.
Giving details of Modi's meeting with Trump, Gokhale said the Prime Minister told the US President that India had reduced oil imports from Iran, which supplied 11 per cent of India's energy.
He said India had done this despite the effect it had on its economy.
The US, in May, ended its waiver to Indian companies from sanctions for importing oil from Iran.
Tensions between the US and Iran have escalated in the recent weeks after two ships were attacked in the Gulf of Oman, for which Washington blamed Tehran.
Talking about India's concerns over instability in the region, Gokhale said India also has its diaspora present there, has energy requirements there and has economic interests there.
"Therefore, it is in India's fundamental interest to ensure peace and stability of the region," the Foreign secretary said.
He said the Prime Minister also pointed out that India has deployed some of its Navy ships in the region to protect the Indian flagged vessels passing through the Gulf and the straits of Hormuz.
This was appreciated very much by Trump and they had a brief discussion, Gokhale added.
The US President expressed his hope that oil prices will remain stable, he said.
Trump talked about "what United States was doing to ensure that stability was maintained in the Gulf and that oil prices were stable and both sides agreed that we would remain in touch on the issue of Iran and we will continue to have mutual discussion on how we ensure regional peace and stability," the Foreign Secretary said.
On 5G, there was a brief discussion, essentially on the technical and business opportunities that this new area provides for cooperation between India and the United States, he said.
"The Prime Minister outlined that we are going to be a billion users of this technology and in that sense India is the second largest market in the world. The way India moves or the way whatever choices India makes will essentially determine the way the global trend will go," Gokhale said.
To a question, the Foreign Secretary said there was no discussion on India's deal with Russia for procurement of five S-400 missile defence systems, which the US wants to be scrapped.
Asked whether the S-400 issue could hurt relations with the US since India is determined to go ahead with the deal, he replied, "Let me be very clear about this. No one issue is going to impact on the larger strategic relationship between India and United States. This is a relationship which is deep, which is broad."
He went on to add, "We have some issues, we will work through them but no one issue is going to, in any way, have any impact."
According to the White House, the two leaders declared that their countries were "central to global peace and stability" and pledged to "provide strong leadership to address global challenges and build prosperity for their citizens in the decades to come".
( With inputs from IANS )