The International Atomic Energy Agency (IAEA) said its inspectors had verified the 300kg (660lb) cap had been exceeded.
Persian stepped up production of enriched uranium, which is used to make reactor fuel and potentially nuclear weapons, in response to reinstated US sanctions.
European nations have warned that any violation will bring consequences.
The deal allows for the re-imposition of multilateral sanctions that were lifted in return for Iran limiting its nuclear activities.
The mechanism, known as Instex, essentially allows goods to be bartered between Iranian and foreign companies without direct financial transactions. It became operational on Saturday, but Mr Zarif said it did not meet Iran's needs.
The development comes at a time of high tension in the Middle East, with Iran shooting down a US drone over the Strait of Hormuz in disputed circumstances, and the US accusing Iran of being behind two sets of attacks on oil tankers.
BBC/LNP

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