"The deal has been finalized, the money has already been transferred to the accounts of the Iranian Atomic Energy Organization", he said.
The report pointed to a weapons shipment that was seized by the US Navy in the Gulf of Oman.
Iran's chief nuclear envoy Abbas Araqchi said the world powers with whom it concluded a deal previous year to shrink its atomic programme in exchange for sanctions relief had agreed with Tehran on Tuesday that obstacles to banking with Iran should be removed.
Zarif's remarks, carried by the semi-official Fars news agency on Tuesday, followed revelations the day before of the confidential document - an add-on agreement to the nuclear deal signed previous year with world powers - that Iran gave the IAEA.
The report mentioned an intercepted Iranian arms shipment to rebels in Yemen and a violation of travel restrictions on Iranians such as the head of its al-Quds Force, who was recently seen in Iraq. The document says that 11 to 13 years into the 15-year agreement, Iran can replace the 5,060 inefficient centrifuges it now uses to enrich uranium with up to 3,500 advanced machines.
But a comparison of outputs between the old and newer machines shows the newer ones work at double the enrichment rate. That means they would reduce the time Iran could make enough weapons grade uranium to six months or less from present estimates of one year.
While the document doesn't say what happens with centrifuge numbers and types past year 13, U.S. Energy Secretary Ernest Moniz told The AP that Iran will be free to install any number of advanced centrifuges beyond that point, even though the nuclear deal extends two additional years.
However, the State Department's Toner said the supposed "secret document" referred to in the report "appears to be Iran's long term enrichment R&D plan that was submitted by Iran to the IAEA as part of its initial Addition Protocol declaration".
"As of today, one year later, a program that so many people said will not work, a program that people said is absolutely doomed to see cheating and be broken and will make the world more unsafe, has, in fact, made the world safer, lived up to its expectations, and thus far produced an ability to be able to create a peaceful nuclear program with Iran living up to its part of this bargain and obligation", said Kerry, one of the main architects of the accord.
This week, a group of 75 national security leaders released a letter to Obama extolling the deal's accomplishments and called for using the landmark opening to expand engagement with Iran.
In selling the deal to skeptics, the USA administration said it is tailored to ensure that Iran would need at least 12 months to "break out" and make enough weapons grade uranium for at least one weapon.
"God willing, when the complete text of the document is published, it will be clear where we will stand in 15 years", he said.
The document also notes that Iran will greatly expand its work with centrifuges that are even more advanced, including large-scale testing in preparation for the deal's expiry 15 years after its implementation on January 18.
Yet, he underlined that "the breakout time does not go off a cliff nor do we believe that it would be cut in half, to six months, by year 11".