Unfazed, the administration has warned that even allies would face sanctions if they didn't show significant progress in reducing Iranian oil purchases by November 4, ruling out broad exemptions or waivers.
In May, the United States pulled out of a 2015 deal between world powers and Tehran under which worldwide sanctions were lifted in return for curbs on its nuclear program.
The US is now also pushing Pyongyang to scrap its nuclear capabilities after President Donald Trump and North Korea's leader Kim Jong Un agreed a vague commitment to "denuclearisation of the Korean Peninsula" at their landmark summit in June.
Iran says the sanctions are endangering lives by blocking the sale of new planes and spare parts for its ageing fleets.
President TrumpDonald John TrumpPastor at Trump rally prays to shield Trump from "jungle journalism" Bill Russell: Being criticized by Trump is the "biggest compliment you can get" Salmon farmers in California fear Trump will destroy their industry MORE pulled the US out of the Obama-era nuclear deal, which offered sanctions relief in exchange for Tehran reining in its nuclear program.
The controversial move was preceded by a deadly crush of Hajj pilgrims in September 2015, which killed more than 460 Iranians. The Iranian rial has fallen to 99,000 to the USA dollar despite a government-imposed rate of 44,000.
Outrage by Iran's leaders when Trump took the decision in May is now being supercharged by small street protests against the government over the economy and the threat of more as the situation worsens.
The first phase hits on Tuesday with blocks on financial transactions and imports of raw materials, as well as sanctions on Iran's automotive sector and commercial aircraft purchases.
Hardship is coming to Iran.
China's Unipec, the trading arm of Sinopec, has suspended crude oil imports from the United States.
The exercise was held with aim of "controlling and maintaining the security of the global waterway of the Persian Gulf and the Strait of Hormuz, and to proportionately counter any threats by the enemy", semiofficial Tasnim news agency reported.
The strait connects the Persian Gulf to the Arabian Sea.
Iranian President Hassan Rouhani has warned the US against any attempt to stop Tehran's oil trade, threatening to block the strategically important Strait of Hormuz. The US Energy Information Administration calls it "the world's most important oil transit chokepoint", with 20% of oil traded worldwide moving through the waterway, which is about 30 miles wide at its narrowest point.