"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.
The oil and financial sanctions end all the economic benefits the United States granted to Tehran for its 2015 nuclear deal with world powers, even though Iran has been abiding by the accord that saw it limit its enrichment of uranium.
Another said: "America is not our enemy, our enemies have taken us as hostages in our own home [country]". Contrary to what he called "fueled misinformation", he stated that SWIFT, "if it provides financial messaging services to certain designated Iranian financial institutions...could be subject to sanctions".
But Mr Rouhani struck a defiant tone, saying that Iran would "continue selling oil". When questioned about whether the European Union or other nations or jurisdictions would receive waivers (or SREs, "significant reduction exemptions"), he answered "T$3 he EU will not be receiving an SRE".
"Unlike in prior administrations, we will ensure that the money is not spent on illicit activities, that there isn't any leakage in these escrow accounts, and we will work closely with countries to encourage the sale and purchase of humanitarian goods to benefit the Iranian people".
The UK, Germany and France - which are among the five countries still committed to the nuclear pact - have all objected to the sanctions, the BBC said. "The new sanctions might prove to be costly if the Kingdom of Saudi Arabia, with spare production capacity, is unable or unwilling to put more oil in the market".
"This is an economic war against Iran but".
Benjamin Netanyahu said Monday at parliament that the Trump administration's decision to restore sanctions was already having an effect.
Also Monday, Iran's Telecommunication Minister Mohammad Javad Azeri Jahromi and his deputy, Hamid Fatahi, both tweeted about a cyberattack targeting the country's communications infrastructure, without elaborating.
Speaking at a daily news briefing in Beijing, Chinese foreign ministry spokeswoman Hua Chunying said China's lawful trade cooperation with Iran should be respected, and expressed regret at the re-imposition of sanctions.
South Korea was also granted an exemption from Washington to continue financial transactions with the sanctioned Iranian central bank to facilitate oil imports, according to the official.
Washington is re-imposing the sanctions after Mr Trump in May pulled out of a 2015 accord aimed at curbing Iran's nuclear ambitions.
Telecommunication Minister Mohammad Javad Azeri Jahromi and his deputy, Hamid Fatahi, both tweeted about the attack on Monday - the same day US sanctions on the country once lifted by the nuclear deal resumed.
But US Secretary of State Mike Pompeo vowed to push Iran's oil sales to zero.
The other major oil producing countries are expected to ramp up production to try and compensate for Iran's anticipated decline in output. "But they're not doing very well", he said. "We are intent on making sure the Iranian regime stops siphoning its hard currency reserves into corrupt investments and the hands of terrorists".