Mohammad Javad Zarif's remarks came during a joint news conference with visiting EU foreign policy chief Federica Mogherini aimed at ensuring that the historic agreement swiftly takes effect.
As the European Union's high representative, Mogherini was intricately involved in the long-running diplomacy that culminated in a July 14 accord between Iran and six world powers.
Her trip to Tehran came days after US Secretary of State John Kerry was grilled by lawmakers in Washington who effectively accused him of being duped in the talks by Zarif and Iran's other negotiators.
The past week has also seen hardline elements in the Islamic republic, including the commander of the powerful Revolutionary Guards force and MPs, raise concerns about the agreement's terms.
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Under the deal, Iran must take measures at its nuclear facilities to satisfy UN monitors of their peaceful nature.
In return, the P5+1 powers in the talks -- Britain, China, France, Russia and the United States plus Germany -- must finalise the mechanism for lifting UN and Western sanctions.
"Iran will continue to cooperate with the IAEA," he said, referring to the UN nuclear watchdog.
"I hope the EU and United States will continue to implement their commitments," he added.
Asked about accusations made in some of Iran's conservative media that the agreement breaks supreme leader Ayatollah Ali Khamenei's "red lines" for the talks, Zarif moved to allay such claims.
"Iran has stuck to its obligations and Iran is going to do the same when it comes to implementing the deal," he said, acknowledging that "some people in Iran have some doubts about some countries, particularly the US, to implement seriously and precisely".