Iran late past year inaugurated the port on the Indian Ocean, which is being built largely by India and is expected to provide a key supply route for Afghanistan while allowing India to bypass rival Pakistan to trade with Central Asia and Africa.
The first phase of the strategically-located project was inaugurated in December previous year.
On Monday, the United States restored sanctions that target Iran's oil exports, as well its banking and transport sectors.
Pompeo said eight countries would be granted waivers from the sanctions as they had significantly reduced their purchases of Iranian crude over the past six months.
"After extensive consideration, the Secretary (of State) has provided for an exception from imposition of certain sanctions under the Iran Freedom and Counter-Proliferation Act of 2012, with respect to the development of Chabahar Port, construction of an associated railway and for shipment of non-sanctionable goods through the port for Afghanistan's use, as well as the country's continued imports of Iranian petroleum products", a State Department spokesperson told PTI.
This waiver will bring some measure of relief to India, which had been discussing a sanctions exemption for Chabahar having signed an agreement with Iran and Afghanistan in May 2016 for the port's development.
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The Persian version said the U.S. "will regret this unwise move" and emphasised that the sanctions were aimed at "separating people from each other and from the establishment".
New Delhi has poured $2 billion into development in Afghanistan since the 2001 USA -led overthrow of the Taliban government.
"Delhi also made clear that it does not support Iran's destabilising activities in the Middle East or an Iranian nuclear weapons program, and that any involvement in Chabahar will not advance those two agenda", he said.
Any return to limiting supply would follow a June decision by the OPEC-led group to relax output curbs in place since 2017, after pressure from U.S. President Donald Trump to cool prices and make up for losses from Iran. It understands India's national security interests.
"This exception relates to reconstruction assistance and economic development for Afghanistan".
"We have weathered hard times in the face of 40 years of American hostility relying exclusively on our own resources, and today we and our partners across the globe will ensure that our people are least affected by this indiscriminate assault", he said.