"We have been clear that Iran has been performing its obligations on [sic] the deal", he was quoted as saying by Iran's IRNA news agency.
"It is the US's and Europe's interest to prevent nuclear proliferation in a volatile region and to maintain the transatlantic partnership as a reliable and credible driving force of world politics", the MPs wrote.
The 2015 Joint Comprehensive Plan of Action, the official name for the Iran nuclear deal, saw economic sanctions lifted on Iran in return for strict limits on its nuclear programme.
Tehran has vowed to remain in the deal as long as the other parties respect it, but will "shred" it if Washington leaves.
German Chancellor Angela Merkel and French President Emmanuel Macron will head to Washington next week to press the Trump administration to stay in the accord signed by the three European powers, Russia, China and the United States.
Zarif reiterated that European countries need to impose pressure on the U.S. in order to compel and encourage it to implement what it pledged under the deal, adding: "Unfortunately, it hasn't been doing that".
"Teheran's reaction to America's withdrawal of the deal will be unpleasant", Iranian state TV quoted Iranian Foreign Minister Mohammad Javad Zarif as saying in NY.
Macron, who arrives in Washington Monday for a state visit while transatlantic tensions persist over trade, Syria and Iran, said he was mindful of how France was the first worldwide ally of American revolutionaries during their war for independence.