On the US sanctions, the government has been maintaining that it will go by what is in the country's national interest.
It was not immediately clear whether Gokhale requested the US delegation to consider providing India with some waiver from the sanctions.
The talks in New Delhi came on a day US treasury secretary Steven Mnuchin reportedly said in Washington that US may consider providing waivers from the sanctions to some countries which require time to cut import of oil from Iran.
India has also been hoping that it will get some relief from the sanctions.
The US delegation is here as part of the Trump administration's efforts to reach out to countries who are major importers of oil from Iran.
The government is yet to take a decision on cutting import of oil from Iran in compliance with the US sanctions.
There were no official comments from the Indian and the US sides.
On Monday, India and Iran had extensive deliberations on ways to deal with the impact of the US sanctions and decided that both the countries will maintain the momentum of mutually beneficial bilateral cooperation.
In May, the Trump administration had pulled out of the Iran nuclear deal and brought back economic sanctions against Tehran.
The US has told India and other countries to cut oil imports from the Gulf nation to "zero" by November 4 or face sanctions. India is yet to take a call on complying with the US sanctions on Iran.
The first set of US sanctions will kick in from August 6.
Iran is India's third-largest oil supplier after Iraq and Saudi Arabia. Iran supplied 18.4 million tonnes of crude oil between April 2017 and January 2018 (first 10 months of fiscal 2017-18).
Earlier this month, government sources said India is looking at the possibility of falling back on the rupee-rial arrangement for importing oil from Iran in the wake of US sanctions.
The rupee-rial arrangement was used to buy oil from Iran before sanctions were lifted against it three years ago.
Under the mechanism, India used to pay in euros to clear 55 per cent of its dues through Ankara-based Halk bank. The remaining 45 per cent payment was remitted in rupees in accounts Iranian oil companies had with the Uco Bank.
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