The newly reimposed sanctions target transactions with USA dollar banknotes; trade in gold and precious metals; direct or indirect sales of graphite and metals such as steel and aluminum; certain transactions related to the Iranian rial; certain transactions related to issuing Iranian sovereign debt; and Iran's automotive sector.
But a second tranche to return to effect on November 5 covering Iran's vital oil sector, could be far more damaging - even if several key customers such as China, India and Turkey have refused to significantly cut their purchases.
Trump pulled the USA out of the deal limiting Iran's nuclear activities.
Iran accused the U.S. of reneging on the nuclear agreement, signed by the Obama administration, and of causing recent Iranian economic unrest.
The EU said it is simultaneously implementing a "blocking statute" as the new sanctions take effect, stopping European companies from complying with the US sanctions unless they have permission to do so. Russian Federation and China also signed on to the 2015 deal. "I am asking for WORLD PEACE, nothing less!" he tweeted. The last time Iran was sanctioned, it lost half of its exports, which have now returned to 2.4 million barrels per day.
"If there is sincerity, Iran has always welcomed dialogue and negotiations", Rouhani said, according to CNN.
"The United States is fully committed to enforcing all of our sanctions, and we will work closely with nations conducting business with Iran to ensure complete compliance".
Foreign Office minister Alistair Burt has moved to reassure businesses they will not face legal action in connection with deals with Iranian firms.More news: Manchester United To Offer Anthony Martial In Return For Defender
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Iran's president said the measures were "psychological warfare" which aimed to "sow division among Iranians".
European Union officials, however, were quoted on Monday as saying that a number of other countries had asked them for details on the blocking regulations as they also explore ways to bypass sanctions.
He said: "If you stab someone with a knife and then you say you want talks, then the first thing you have to do is remove the knife. But talks need honesty".
He said the USA has long designated Iran as the world's foremost state sponsor of terrorism.
Iran's Foreign Minister Mohammad Javad Zarif told reporters the global reaction to Mr Trump's move showed that the U.S. was diplomatically "isolated", but acknowledged the sanctions "may cause some disruption".
"If Iran were really serious they'd come to the table".
Few American companies do much business in Iran, an enemy of the United States since its 1979 Islamic Revolution, so the impact of any sanctions depends on Washington's ability to block European and Asian firms from doing business there.
USA officials estimate that almost 100 global companies have announced their intent to leave the Iranian market, particularly in the energy and the finance sectors, he said.
It sets out to allow firms to recover damages from bodies that enforce U.S. sanctions - and bans companies from complying with United States sanctions without European Union permission.