On Friday, Mr Trump agreed to waive sanctions against Iran that were lifted as part of the global deal but said it would be the last time unless conditions were met to fix what he called "significant flaws" in the deal.
Iran argues that continued United States sanctions on non-nuclear areas such as human rights and missile testing have effectively barred Iran from gaining numerous financial benefits expected from the deal.
"This is a last chance", Donald Trump said in a statement, Efe reported.
It also said Iran would not allow the deal to be linked to other issues, after Trump suggested that the sanctions relief under the deal be tied to Iran limiting its long-range ballistic missile program.
Mr Zarif responded on Twitter that the deal was not renegotiable and that Mr Trump's stance "amounts to desperate attempts to undermine a solid multilateral agreement". "Rather than repeating exhausted rhetoric, United States must bring itself into full compliance - just like Iran".
Ryabkov said the US withdrawal from the deal would damage other worldwide agreements.
Trump and his top advisers have been negotiating with United States lawmakers on Capitol Hill to try to change sanctions legislation so that he does not face a deadline on whether to recertify Iranian compliance with the nuclear deal every 90 days. The next sanctions waivers are due in May.
This would not entail negotiations with Iran but would be the result of talks with European allies, the official said.
The EU said it would hold internal consultations and was "committed to the continued full and effective implementation" of the deal. The Treasury Department's action hits 14 Iranian officials and companies and businessmen from Iran, China and Malaysia, freezing any assets they have in the US and banning Americans from doing business with them.
Since the historic deal was signed in Vienna, the IAEA has repeatedly confirmed Iran's compliance with its commitments under the JCPOA, but some other parties, especially the USA, have failed to live up to their undertakings. "No one should doubt my word".
"We are gradually coming to the conclusion that an internal decision by the USA to leave the (Joint Comprehensive Plan of Action) has already been made or is close to being made", Ryabkov said in an interview with Interfax news agency.
The decision had been expected since earlier this week.
The US Congress requires the president to decide periodically whether to certify Iran's compliance with the deal and issue a waiver to allow US sanctions to remain suspended.
The deal would help uphold the worldwide non-proliferation regime, maintain regional peace and stability and solve "other hot issues" around the world, he said.