Europeans, also signatories to the JCPOA agreement, have said they are determined to save the text, with the EU saying on Tuesday it aimed to "protect European economic operators engaged in legitimate business with Iran".
Iran's President Hassan Rouhani - who insists that its nuclear programme is entirely peaceful - has accused Mr Trump of waging "psychological warfare", and ruled out face-to-face talks with him while the sanctions remain in place.
But that has proven hard, and European companies have quit Iran, arguing that they can not risk their US business.
Ri was also quoted as describing the sanctions against Iran as "inappropriate and contrary to global standards".
During his meeting with North Korean Foreign Minister Ri Yong-ho in Tehran on Wednesday, Rouhani warned him that United States was "an unreliable and untrustworthy" negotiating partner that did not honour "any of its commitments". We want to keep our journalism open and accessible and be able to keep providing you with news and analyses from the frontlines of Israel, the Middle East and the Jewish World.More news: Lombok natural disaster : Victims 'buried alive' as number of dead rises to 131
Rouhani said Iran and North Korea have had common views during many "sensitive global periods" and said Iran will work to improve ties and worldwide cooperation with North Korea.
"Reimposition of nuclear-related sanctions through today's actions further intensifies pressure on Tehran to change its conduct", Trump said Monday.
"If there is one piece of global agreements on nuclear non-proliferation that is delivering, it has to be maintained".
Before Trump withdrew from the deal, France's Emmanuel Macron, Germany's Angela Merkel and Britain's Theresa May had pleaded with the president to give them leeway to address his concerns in a "side deal", a new negotiation to limit Iran's missiles, extend the term of the original Iran deal, and confront Iran's support for terrorism. But he says the USA military is "paying attention", and will "remain ready to protect ourselves".
North Korea's Ri has also delivered a scathing attackon the Trump administration for enforcing sanctions at the same time as trying to negotiate the denuclearizaton of North Korea.
Meanwhile, the White House has said Pyongyang has yet to take a decisive effort to denuclearize.