In a statement carried by the state-run IRNA news agency, the Foreign Ministry said Iran "will not accept any change in the deal, neither now nor in future", adding that it will "not take any action beyond its commitments".
"Today, I am waiving the application of certain nuclear sanctions, but only in order to secure our European allies' agreement to fix the awful flaws of the Iran nuclear deal". Trump is also waiving other US penalties covered by the agreement, including on Iran's oil and gas sectors, which were up for renewal next week.
The Iranian Ministry of Foreign Affairs on Saturday criticised the fresh sanctions imposed by the United States by calling them illegal and hostile, and warned that they would receive a serious reaction by the Islamic republic.
It did not specify what any retaliation might involve.
Trump said on Friday he will extend sanctions relief on Iran under the 2015 nuclear deal for the last time, threatening US withdrawal from the landmark pact unless US Congress and European allies can fix the alleged "disastrous flaws".
Iran says its nuclear programme has only peaceful aims and says it will stick to the accord as long as others respect it.
The 2015 deal, he said, "is not renegotiable".
Trump, who has sharply criticised the deal reached in Barack Obama's presidency, had chafed at having to once again waive sanctions on a country he sees as a threat in the Middle East.
Iran on Saturday rejected any modification of its nuclear deal with world powers after US President Donald Trump demanded tough new measures to keep the agreement alive. To keep the U.S. in the nuclear agreement in the future, senior administration officials said Trump will pressure European partners to agree to impose new conditions on Iranian behavior.
Trump's 'shithole' countries are worth $46.6 billion in trade to America
Democratic senator Dick Durbin also condemned Mr Trump's language during the meeting as "hate-filled, vile and racist ". The African Union responded to President Donald Trump's description of African nations as "shithole countries." .
While Trump approved the sanctions waiver, the Treasury Department announced new, targeted sanctions against 14 entities and people, including the head of Iran's judiciary, Sadeq Amoli Larijani, a close ally of Iran's Supreme Leader Ayatollah Ali Khamenei. "It's going to be complicated to save the deal after this", said one European diplomat, speaking on condition of anonymity.
Britain, France and Germany called on Trump on Thursday to uphold the pact.
The 2015 deal, known as the Joint Comprehensive Plan of Action, was signed by the U.S. under the previous administration of president Barack Obama as well as Iran, China, Russia, Britain, France and Germany.
Republican Senator Bob Corker said "significant progress" had been made on bipartisan congressional legislation to address "flaws in the agreement without violating US commitments".
Trump has argued that Obama, a Democrat, negotiated a bad deal for the United States in agreeing to the nuclear accord.
Iran has said it's not interested in any renegotiation and would nearly certainly view a side agreement between the USA and Europe as a violation of the deal.
Ryabkov's remarks come one day after U.S. President Donald Trump extended sanctions relief on Iran for what he said would be the final time.
The president wants US Congress to modify a law that reviews US participation in the nuclear deal to include "trigger points" that, if violated, would lead to the United States reimposing its sanctions, the official said. Trump wants them to help the US devise a new agreement created to prevent Iran from escalating nuclear activity again next decade, as permitted under the 2015 arrangement reached by President Barack Obama.
The EU said it would hold internal consultations and was "committed to the continued full and effective implementation" of the deal. The other parties to the agreement would have been unlikely to join the United States in reimposing sanctions. The appeal was made after the Iranian Foreign Minister met with European Union foreign ministers and European Union foreign policy chief Federica Mogherini in Brussels on Thursday.