The statement was made days before President Donald Trump's deadline to decide if the USA will remain in the agreement.
"The Iran nuclear deal is not based on trust about Iran's intentions; rather it is based on tough verification, including measures that allow inspectors from the International Atomic Energy Agency (IAEA) unprecedented access to Iran's nuclear program", the British foreign secretary said.
French President Emmanuel Macron says he does not know whether US President Donad Trump will stick to the 2015 Iran nuclear deal.
"Iran is committed to the nuclear deal but if the USA backs off" from the accord "we won't stay either", Ali Akbar Velayati, adviser to Supreme Leader Ayatollah Ali Khamenei, was quoted by state-run Mehr news agency as saying Thursday.
Zarif said the United States has "consistently violated the nuclear deal, particularly by bullying others to prevent businesses from returning to Iran".
Trump is a stern critic of the nuclear deal, reached under his predecessor Barack Obama, and has repeatedly warned that he might ultimately terminate the agreement.
During the press conference, he paraded in front of a huge LED screen, showing what he claimed were a half-ton of documents proving that Iran breached the deal.More news: NBA Playoff Odds: Warriors New Betting Favorites Followed by Rockets and 76ers
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Mr Guterres called on the USA leader not to withdraw from the deal, saying that it risked a real possibility of war if the agreement was not maintained. "So I think we should separate things".
Hamid Baeidinejad, the country's top envoy in London, said Iran would "be ready to go back to the previous situation" if America pulls out of the 2015 pact, as threatened by US President Donald Trump.
Technically, Trump must decide by May 12 whether to renew "waivers" suspending some of the USA sanctions on Iran.
Velayati warned against any attempts to renegotiate in exchange for sanctions relief, saying, "Iran accepts the nuclear agreement as it has been prepared and will not accept adding or removing anything".
Iran has denied ever seeking nuclear weapons and accuses its arch-foe Israel of stirring up world suspicions against it.
"Every detail PM Netanyahu presented yesterday was every reason the world came together to apply years of sanctions and negotiate the Iran nuclear agreement - because the threat was real and had to be stopped", Kerry wrote on Tuesday.
The Iran nuclear deal signed by Tehran and the five permanent members of the UN Security Council - the US, France, Britain, Russia and China - plus Germany on July 14, 2015, imposes strict restrictions on Iran's nuclear program in return for the loosening of economic sanctions. Iranian President Hassan Rouhani has called into question the legitimacy of the USA and Israel making moves to have the deal scrapped after it gained the consensus of five world powers in 2015 in what was widely regarded at the time as a significant diplomatic victory in the global community.