"None of that, I believe, is consistent with that preamble commitment that was made by everyone" in the nuclear deal, he said.
The penalties are created to put pressure on Iran as they continue to deny violating the nuclear deal.
US President Donald Trump has repeatedly lambasted the deal and in a July interview with the Wall Street Journal said he would be "surprised" if Iran was found to be in compliance when he next has to make a determination on the matter in October.
Iran's Supreme Leader Ayatollah Ali Khamenei waves as he gives a speech in Tehran, Iran, on June 3. "Every wrong step by the aggressive regime [the US] regarding the nuclear deal will be met with a response from the Islamic Republic".
Iran's supreme leader has said his country will not be bullied by the United States and will react strongly to any "wrong move" by Washington on Tehran's nuclear deal.
It is obvious that the withdrawal of Iran from the nuclear deal may provoke a new round of the arms race in the Persian Gulf and a serious confrontation of various forces in the Middle East region. Trump had earlier said that the Iran deal is one of the worst he had ever dealt with.
Last month, US Ambassador to the UN Nikki Haley traveled to Vienna to press the IAEA on accessing Iran's military sites; a demand which has been categorically rejected by Tehran.More news: Simon Pagenaud takes Sonoma victory as Josef Newgarden takes title
Reinvigorated by the Donald Trump administration, there is now a full-scale campaign underway in Washington to kill the Joint Comprehensive Plan of Action (JCPOA) and convince the public that it is Iran - not the USA - who is violating the accord.
Iranians residing outside the country can contribute to Iran's glory in cultural, scientific and technological interaction, said Rouhani adding: "What we want from you dear Iranians is to increase your share in Iran's progress more than before".
He noted that the USA has been seeking to use terrorism as a means in the Middle East, but regional nations, particularly the Iraqi and Syrian people, are defeating the vicious scourge, emphasizing that terrorism is on the verge of full elimination in the region.
Shamkhani's remarks came one day after Washington said it would extend the sanctions relief that Iran was granted under the 2015 nuclear deal but would impose new penalties on Iranian individuals and entities over Tehran's ballistic-missile program. The deal lifted crippling sanctions on Iran's economy in return for a reining back of its uranium enrichment program.
If he does not, Congress has 60 days to decide whether to reimpose sanctions waived under the deal.
Speaking to Al-Monitor on condition of anonymity, a senior Iranian source dismissed the idea of Tillerson's State Department having requested the September 20 session, saying, "The meeting was initially requested by Iran to address its grievances about U.S. violations".