Speaking at a meeting with the directors and deputies of the Ministry of Economic Affairs and Finance on Monday, President Rouhani said, "We should break the sanctions very well, and we will do that."
"With the help of the people, and the unity that exists in our society, we have to make the Americans understand that they must not use the language of force, pressure, and threats to speak to the great Iranian nation. They must be punished once and for all," the Iranian president said.
The meeting and remarks came shortly after a new round of US sanctions took effect. The new bans target, among other things, Iran's oil sales and Central Bank. More Iranian individuals have also been targeted by the US Department of the Treasury.
The US measures also include so-called secondary sanctions — punitive measures against third countries doing business with Iran.
US President Donald Trump introduced a first round of "primary" and "secondary" sanctions against Iran and its trade partners in August.
In May, he unilaterally pulled the US out of a multilateral deal with Iran. Two months later, footage reportedly came out
in which Israeli Prime Minister Benjamin Netanyahu claimed he had personally convinced Trump to withdraw from the Iran deal.
Iran struck the deal with originally six world powers and the European Union (EU) back in 2015, agreeing to curb its nuclear program in return for the lifting of restrictions mainly on its oil sales.
Despite the US withdrawal, Iran has stayed in the deal but has stressed that the other parties to the agreement have to work to offset the negative impacts of the US pullout. Europe has been taking a range of measures to meet the Iranian demand for practical guarantees.
President Rouhani said Europe, too, was angry at US policies.
"Today, what the Americans are doing is merely pressure [ordinary] people, and no one else. It's pressure [that is being put] on [the Iranian] people, other nations, other [foreign] businesses, and other governments," he said. "Today, we are not the only ones who are angry at US policies; even European businesses and governments are angered by US policies, too."
The US had since the May 8 withdrawal designated November 4 as the date when it aimed to bring Iran's oil sales down to "zero." However, three days ahead of that much-advertised deadline, the US granted waivers
to eight major state buyers of Iranian crude.
President Rouhani said US officials had in fact conceded defeat.
"They (the Americans) saw that they couldn't replace [Iranian oil on the market]; and even assuming they did not concede defeat and did not grant waivers to countries, we would still be able to sell our oil [because] we have adequate capabilities to do that," the Iranian president said.
'Europeans want Trump gone'
In his Monday remarks, President Rouhani also said he believed that America had never before seen as lawless an administration as that of Trump's.
He said all US administrations had violated international law, but "these (current officials) score on top on the lawlessness rankings."
"I don't recall a group assuming power at the White House that was racist as these," the Iranian president said.
"This is not [just] us who wish for the life of this incumbent administration in the US to become shorter and shorter; their (the Americans') own European allies have told me in [private] meetings that that is one of their wishes," President Rouhani said.
'Dialog needs no intermediary, but US must honor promises'
President Rouhani said that when he was in New York for the annual meeting of the United Nations General Assembly in September, "the leaders of four major countries" sought to broker a meeting between him and the US president. He did not name those leaders.
The Iranian chief executive said, however, that there was no need for mediation.
"Honor your obligations first! We will speak then," Rouhani said, addressing American officials. "We have no problem with talking. If our interlocutor honors its word and promises, what will be wrong with talking?"
He noted that the unilateral withdrawal from the Iran deal has isolated the US.
"Just look at how many countries support the US move and how many don't," he said. "The fact America insists on something and the entire European Union resists that same thing is nothing simple. That means victory for [our] diplomacy and foreign policy."
Earlier, President Rouhani's chief of staff announced that Trump had eight times requested a meeting with the Iranian president while he was in New York but had been rejected all eight times.
'Iran in economic war with US' & 'Iran's economic problems will end'
President Rouhani also said that the Islamic Republic was engaged in "an economic war" with the US.
"We have to stand and fight, and win," he said. "God will make us win."
The Iranian president also said the current economic problems faced by Iran will not continue.
"We will re-launch economic growth. No one should think the trend we have been seeing in the past several months will continue like that. This trend will be stopped."
Iran's national currency has lost some of its value against the US dollar over the past months. While the Iranian rial has partially rebounded, it continues to be at a low exchange rate against the US dollar.