His remarks came at a joint press conference with External Affairs Minister S. Jaishankar, who had earlier said that India has a certain perspective on Iran which also comes from India's geographic location.
"We all know that Iran is the world's largest state sponsor of terror and we know that Indian people have suffered from terror around the world. I think there is a shared understanding of the threat and a common purpose to ensure that we can keep the energy at the right prices," he said.
Pompeo made the remarks in response to a question after Jaishankar said that the global energy supplies should remain predictable and affordable and the visiting US leader was very receptive.
"We have a certain perspective on Iran, obviously from where we are based. US Secretary of State shared with me the American concerns on Iran. Both of us certainly came out much better informed of each other's concerns in that regard," Jaishankar said.
The US had, earlier this year, decided not to renew exemptions to India and some other countries from its sanctions for importing oil from Iran. The exemptions ended on May 2.
India is keen on de-escalation of tensions between Iran and the US and has said earlier that it will take a decision on import of oil from Iran based on its energy security and commercial considerations.
India has been speaking to Irans and asking both sides to de-escalate and refrain from any action that can disturb peace and security.
The situation developing in the region is a matter of great concern to India also because of the presence of the Indian diaspora in the troubled region and it has a strong and legitimate interest that peace is maintained in the region.
The US has imposed new sanctions on Iran following Tehran's downing of an unmanned American drone.
Import of oil from Iran is a commercial decision of the compes and they are unlikely to continue it as it could impact their relations with other countries .
( With inputs from ANI )