"I don´t want to waste my time on answering the rants and whoppers of the brute United States president", Khamenei said in a speech to students in Tehran, published on his Telegram channel.
The deal was also signed by China, France, Russia, Britain, Germany and the European Union.
Ayatollah Khamenei, Iran's highest authority, welcomed their support but said it was not sufficient.
The deal signed in Vienna in 2015 between Iran and six world powers - the U.S., Britain, Russia, France, China, and Germany - saw internationally observed limitations to Iran's nuclear weapons program in return for the lifting of global sanctions.
Iran says it has the right to nuclear energy and insists its nuclear programme is for peaceful purposes only.
The American leader called for the deal to be amended to prevent Iran from developing nuclear weapons or intercontinental ballistic missiles.
Europe, firstly, needs to stand against the US' practical measures regarding the JCPOA, Khamenei said, adding, "Secondly, they should not interfere the Islamic Republic's defense issues".More news: Hurricane Ophelia Matches 124-Year-Old Record
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Iran's highest authority also said Tehran was determined to continue its disputed ballistic missile programme despite the pressure from Europe and the United States to suspend it. Tehran has defended the move, saying the weapons are exclusively for defensive purposes.
Europe "must refrain from entering into our defence issues", Khamenei said. "We do not think it is acceptable for the Europeans to join America in its bullying".
"We see no reason to change anything in the guidelines that we have received from the (IMF) Board and continue to operate in the same manner", Lagarde said on Sunday, responding to a question on Trump's new policy on Iran who has strongly urged the IMF and World Bank not to provide loans or funds to Iran.
"Why do YOU have missiles?"
"Or to ask why Iran has missiles - well, why do you have missiles?"
It has called upon the Islamic Republic not to "undertake any activity related to ballistic missiles created to be capable of delivering nuclear weapons".