The EU's foreign policy chief Federica Mogherini added that the global community must also be united in preserving the deal, which she said helped make the world a safer place and prevent a nuclear arms race in the region.
It also said Iran would not allow the deal to be linked to other issues, after Mr Trump suggested that the sanctions relief under the deal be tied to Iran limiting its long-range ballistic missile program.
Trump and his top advisers have been negotiating with USA 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.
Speaking to reporters earlier Friday, a senior USA administration official said Trump will seek "a follow-on or a supplemental agreement" with European partners to strengthen the deal he has vowed to scrap.
Three officials said the waivers will be accompanied by other, targeted sanctions on Iran for human rights abuses and a stern warning that Trump will pull out of the nuclear deal negotiated by the Obama administration if fixes aren't made by spring.
According to anonymous officials on a conference call with various reporters, Trump will not issue any more waivers after Friday unless specific fixes are made to the Iran deal.
'I never said sh*thole, though I did use tough language,' says Trump
Baltimore Mayor Catherine Pugh said Trump is arguably the most influential person in the country and possibly the world. Those affected have until 2019 to leave the USA or, if eligible, seek alternative immigration status.
He underlined that the deal that was signed in 2015 between Iran, and the P5+1 - Russia, France, China, Britain, the United States, plus Germany, can not be amended and that Moscow will "oppose any attempts to hamper it".
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 United States and banning Americans from doing business with them.
Responding to Trump's speech late Friday, Zarif tweeted: "Rather than repeating exhausted rhetoric, US must bring itself into full compliance - just like Iran". Russia will explain persistently to the US the depravity and viciousness of its sanctions-based policies against Iran and the DPRK, Russia's Deputy Foreign Minister Sergei Ryabkov told TASS on Saturday. Bob Corker (R-TN) and Ben Cardin (D-MD) have been working with White House National Security Adviser H.R. McMaster on an agreement that would keep the Iran deal intact.
Sens. Ted Cruz (R-TX) and Marco Rubio (R-FL) didn't like the idea of waiving Iran's nuclear sanctions.
Crude prices have been rising for weeks, in part amid expectations that Trump might pull the United States from the nuclear deal, which, in turn, would re-instate sanctions against Iran and limit its ability to sell oil overseas.
However, the USA imposed fresh sanctions on 14 individuals and entities over alleged human rights abuses. Those mainly targeted Iranian defense officials, as well as a China-based network the United States says is supporting Iran's missile program.