Tom Cotton of Arkansas, Marco Rubio of Florida and Ted Cruz of Texas - have said the new sanctions aren't tough enough and have drafted legislation that would require the Trump administration to demand that Iran be suspended from the global bank transfer system.
USA officials did not immediately make an announcement as the sanctions took force in the early morning hours of November 5, part of Washington's effort to ramp up pressure on Tehran to "change its behavior" and end what the United States says is its "malign" activities in the region.
Iran has greeted the reimposition of USA sanctions with air defence drills and an acknowledgement from the president, Hassan Rouhani, that the country faces a "war situation", raising tensions in the Middle East.
Hours earlier, Trump called the sanctions the toughest ever imposed by the United States against Iran.
"The expected United States waiver for India is a good development that should allow the country to continue getting its share of oil on attractive terms from Iran".
Salami made the remarks on a day when the authorities in Iran organize anti-U.S. gatherings nationwide, unleashing slogans to mark the 1979 seizure of the US embassy in Tehran.
"We are in the war situation", Rouhani said.
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South Korea has been granted a waiver from United States sanctions on Iranian oil, a government official said on Monday.
The Donald Trump administration's decision to issue waivers also marked a significant reduction from the Barack Obama administration, which issued such exemptions in 2012 to 20 countries over 3 years during last sanctions. The other parties to the deal - Britain, France, Germany, China and Russian Federation - say they will not leave.
The bill was meant to pave the way for Iran to accede to the United Nations' Terrorism Financing Convention, thus removing a major point of USA criticism and giving European allies more leeway to develop a financial mechanism aimed at contravening the sanctions.
Iran's economy has been hit hard, with the country's currency, the rial, plummeting in value, leading to some street protests in Iranian cities. America should learn that it cannot use the language of force against Iran.
Iran's military was also quoted as saying it would hold air drills on Monday and Tuesday to prove the country's defensive capabilities. "We have to stand to win".
European powers which continue to back the nuclear deal said they opposed the reapplication of sanctions and major oil buyer China said it regretted the move.
"The Iranian people will prove to them how loyal they are to their Supreme Leader (Khamenei) and that they will never abandon him". In fact, the USA has indicated intent of supplying $2.5-3 billion oil and gas at short notice if India needed it to meet the shortfall arising out of cut in Iranian oil imports.
Washington's top diplomat refused to comment on what specific actions the Trump administration may take against Moscow and Beijing, should both countries decide to continue to do business with Tehran.