"What the United States is doing, in addition to being unpredictable -- which might sometimes work -- is proving that it is unreliable," Zarif told CNN.
The deal, agreed in 2015 between Iran and six world powers -- the United States, China, Russia, France, Britain and Germany -- lifts economic sanctions put in place in 2005 in exchange for curbs to Tehran's nuclear program.
The International Atomic Energy Agency (IAEA) is responsible for verifying that Iran meets the terms of the agreement.
"Frankly, that deal is an embarrassment to the United States, and I don't think you've heard the last of it," he told the UN General Assembly Tuesday.
The president cast further doubt over the deal after the Islamic republic tested a new medium-range Khoramshahr missile yesterday.
"Iran just test-fired a Ballistic Missile capable of reaching Israel. They are also working with North Korea. Not much of an agreement we have!" Trump tweeted.
But Zarif brushed off the threat, saying Washington cannot act alone to end the agreement.
"It's not even a multilateral treaty. It's a Security Council agreement and the United States is a member of the Security Council."
The foreign minister added that Donald Trump's certification of whether Iran is abiding by the deal -- due mid-October -- is an "internal procedure" that in itself does not endanger the agreement.
"The only authority that has been recognized in the nuclear deal to verify is the IAEA," he said.
But according to diplomats, "non-certification" by Trump would lead to re-imposition of sanctions and the "political death" of the agreement.
"Iran has a number of options, which include walking away from the deal and going back with greater speed with its nuclear program, which will remain peaceful -- but which will not address and accept the limitations that we voluntarily accepted over our nuclear program," he said.
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