During the meeting, Rouhani also said the Trump administration is "mistaken" to think that its "maximum pressure" campaign could bring about regime change in the country.
He added that "this illegal restriction is part of the overall U.S. policy of pursuing economic terrorism against the Iranian people and exerting pressure on their representatives".
Iran on August 6 asked the United Nations to push back on USA sanctions and the Islamic republic's President Hassan Rohani said restrictive measures must be lifted first before negotiations can start about the country's nuclear program.
Iran's president said last week that Iran was ready for the worst in an uphill struggle to salvage its nuclear deal, struck in 2015 with world powers, including France.
The Iranian president also cautioned the Trump administration against wading into war.
"Iran only shoots the aggressors which can be drones, air crafts, marine vessels or etc.", he said. "The British vessels had always been [deliberately] making mistakes in maritime traffic and were overlooking" rules, he said.
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"Whether they want to come into the JCPOA or not, it's up to them", said Rouhani, referring to the 2015 nuclear deal known formally as the Joint Comprehensive Plan of Action. "You (Americans) can not harm our security and expect security for yourself in return", Rouhani said. At the height of the crisis, US President Donald Trump called off air strikes against Iran at the last minute in June after the Islamic republic's forces shot down a US drone Â·Rouhani said in any talks the Americans should be ready to negotiate fairly.
"Security for Security, peace for peace, a strait for a strait and oil for oil", Rouhani emphasized.
Iran has reacted to renewed USA sanctions meant to strangle its oil trade by retreating from some of its commitments to limit its nuclear activity made under the deal - known officially as the "Joint Comprehensive Plan of Action", or JCPoA - in return for a lifting of multilateral economic sanctions. "You can not say that you won't allow our oil to be exported".
Washington can not force the Iranian people to change their views through sanctions and pressure, he was quoted as saying. "Today the whole nation is behind our foreign minister", he said.
"Sanctioning a foreign minister means failure in talks", Rouhani added.
Zarif said on Monday that he had turned down the offer despite a threat of being hit with sanctions within two weeks.