"The last set of sanctions lifted under the bad 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.
He said he could not rule out that the US administration would extend the waivers beyond six months.
They will hit oil exports, shipping and banks, and make it hard to do business with the oil-rich nation.
But Mr Rouhani struck a defiant tone, saying that Iran would "continue selling oil".
"Petrochemicals are key to our economy, and we stressed that if we're hit by the Iran sanctions, it would pose grave challenges to our whole economy", said the official who spoke on condition of anonymity.
Pompeo said they are created to "alter the Iranian regime's behavior", especially its support of terrorist groups like Hezbollah. But there are doubts how successful this will be.
The US began re-imposing sanctions on Tehran after President Donald Trump withdrew the country from the Joint Comprehensive Plan of Action (JCPOA) on the Iranian nuclear program in May, branding the deal "defective at its core". But "Iran has weathered multiple rounds of sanctions before".
The remaining members believe the agreement is working as intended and is keeping Iran from obtaining nuclear weapons for now.
President Trump says that he wants to get Iran back to the negotiating table.
The move has raised tensions in the Middle East as America's maximalist approach to the Islamic Republic takes hold.
What could the impact be?"The tougher they are on us, the more resistant we become".
Most of the worldwide firms who lined up to work in Iran after the 2015 deal have been forced to leave, including France's Total, Peugeot and Renault; and Germany's Siemens.
After initially promising to drive the country to zero exports of oil, the USA has offered a waiver to eight buyers of Iranian crude, a move that Secretary of State Mike Pompeo defended yesterday.
In parallel with the imposition of the crude oil sanctions, the US Treasury Department is placing more than 600 Iranian individuals and entities on a black list.
Iraq and Turkey have also previously said they expect to receive waivers, while news agencies have reported that Afghanistan, India, Italy, and Japan were likely to be granted exemptions.
How do other countries see it?
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.
The secretary of state dismissed suggestions from experts, cited by the Fox New interviewer, that India and China will never stop buying oil from Iran.
The ghost of USA sanctions on Iran seems to have calmed down at least for major energy importing countries like India.
Mr Pompeo has said that over 100 big global companies had withdrawn from Iran because of the looming sanctions. The other signatories to the nuclear deal have demanded that Iran accede to the FATF.
What has the reaction been in Iran?
But on the fringes of the crowd, chants of "Death to America" were lackluster, and the protesters appeared simply to be going through the motions.
The seizure of the USA embassy by radical students was a key stage in the Islamic revolution of 1979, leading to a 444-day hostage crisis that permanently damaged relations between Washington and Tehran.