Trump has threatened not to renew the 2015 accord, which curbed Iran's nuclear programme in exchange for sanctions relief.
His threats have prompted pressure from European officials ahead of a May 12 deadline for his decision.
"We have welcomed the insistence of the European Union on keeping America in the JCPOA (nuclear deal)," said Ali Shamkhani, secretary of Iran's Supreme Council for National Security, in a televised press conference.
"But if this means degrading the Islamic republic of Iran or paying a ransom to Trump, the Europeans are making a strategic mistake," he said.
The European parties to the agreement -- Britain, France, Germany and the European Union -- have been trying to convince Trump to stick to the accord.
French President Emmanuel Macron is currently in Washington, hoping to address Trump's concerns and keep the US in the deal.
The White House has demanded tighter restrictions on Iran's regional behaviour and its nuclear and missile programmes.
But Iran says any talk of curbing its missile programme -- which is central to its defence systems -- is off limits.
"The Islamic republic of Iran will not allow any country, under any circumstances, to cross its red lines," said Shamkhani.
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