The Trump administration has said more than 50 foreign companies have withdrawn their business from Iran since Trump announced the USA was withdrawing from the 2015 nuclear deal between Iran and the United States, Germany, France, Britain, China and Russian Federation.
According to Lavrov, the decision particularly concerns small and medium-sized companies.
Zarif did not elaborate but Iranian officials have repeatedly accused the USA of imposing illegal sanctions on Iran after pulling out of the nuclear deal as well as breaching the deal before the pullout.
"Everyone agrees that this [US sanctions - Ed.] is an absolutely illegal and unacceptable policy, but, of course, this can hardly be changed and there will be enough struggle in trade, economic and political spheres", the minister said.
"We're using every element of American power to try to achieve the ends, to try to get Iran to behave in a way that is rational and normal", Pompeo said.
The blocking statute is due to enter force on August 6, when the first set of USA sanctions are due.
The Trump administration is pushing countries to cut all imports of Iranian oil from November when the United States reimposes sanctions against Tehran, after Trump withdrew from the 2015 nuclear deal agreed between Iran and six major powers, against the advice of allies in Europe and elsewhere.
As part of the actions against Tehran, the president also announced new economic and financial sanctions, which will take effect next month.
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They said India is looking at the possibility of falling back on the rupee-rial arrangement for importing oil from Iran in the wake of USA sanctions.
Shipping to Iran and ports in the country are also coming under the USA sanctions.
French Economy Minister Bruno Le Maire told Le Figaro on Friday that after the USA dismissed the European request, he had asked for at least more time before the sanctions kicked in, but that too was rejected.
According to sources, to deal with impact of USA sanctions, India could revive rupee-rial arrangement for importing oil from Iran. That's something that Treasury and State will be doing.
In a letter to European governments, US Secretary of State Mike Pompeo said the US rejected the appeal because it wants to exert maximum pressure on Iran, noting that waivers would apply only if they benefited US national security.
Ministers from Germany, France, the United Kingdom and European Union last month requested broad carve-outs from Washington's sanctions for sectors including healthcare, finance, automotive and energy doing business with Iran.
Thus, States will enact more sanctions against Iran in early August, and European companies will also be affected by these sanctions.