"The last set of sanctions lifted under the awful nuclear deal will come back into force, including powerful sanctions on Iran's energy, shipping, and shipbuilding sectors, and sanctions targeting transactions with the Central Bank of Iran and sanctioned Iranian banks", the President said.
"America wanted to cut to zero Iran's oil sales ... but we will continue to sell our oil ... to break sanctions", Rouhani said.
The Trump administration is also reimposing sanctions on the Iranian regime, effective today.
Hours before the fresh sanctions went ahead, thousands of people in Iran marked the anniversary of the 1979 hostage-taking at the U.S. embassy by carrying placards mocking Trump and burning American flags and fake dollars.
However, the U.S. is expected to give a short-term waiver to eight countries which could include India because of its commitment to significantly reduces the import of oil from Iran.
France, Germany, Britain, and the European Union issued a joint condemnation Friday of the U.S. move, vowing to protect European companies doing "legitimate" business with Tehran.
Iran's Foreign Ministry spokesman Bahram Ghasemi also predicted the sanctions will actually work against America's interests.
President Trump's decision to withdraw the United States from the 2015 nuclear agreement has been widely condemned by the global community.
This is set to hit the economy hard, as the sanctions will be imposed on oil exports, shipping and banks. Wallace noted that "there are a lot of experts who believe that India and China are never gonna stop buying oil from Iran". But he said the eight unidentified nations "need a little bit more time to get to zero".
In contrast, with the US-EU trade wars toned down, most large EU businesses are cooperating with US sanctions against Iran. Other parties to the deal, including Britain, France, Germany, China and Russian Federation, have said they will not leave.
"We are in a situation of economic war, confronting a bullying power".
Senior Iranian officials have dismissed concerns about the impact to its economy.
Iran has dismissed these charges and continues to keep its stand that its nuclear programme is for peaceful purposes.
He said he could not rule out that the USA administration would extend the waivers beyond six months.
Second, although Saudi Arabia has said it will increase capacity by more than a million barrels...
While not threatening to resume higher enrichment, Iranian officials in recent months have said this could resume at any time - and faster than before.
US Secretary of State Mike Pompeo announced on Friday the United States would grant temporary waivers to eight countries to allow them to continue importing oil from Iran after November 5, adding that six of the countries agreed to significantly reduce imports of Iranian oil, while two others plan to halt their imports entirely.
HBO issued a warning to Trump after the U.S. president tweeted an image of himself looking off-camera while striding forward on top of a moody grey background, with the words "Sanctions are coming".
It is 39 years since 52 American citizens were taken hostage and held for 444 days after hardline students stormed the United States embassy.