"My team, the assistant to (EU foreign policy chief Federica) Mogherini and the other representatives of the 5+1 will meet next Tuesday to begin drafting the text," he told Spanish officials in Madrid, where he is on a visit, in remarks carried by Iran's ISNA news agency.
He did not say where the talks would take place.
After marathon talks in Lausanne, Switzerland, Iran and the P5+1 (Britain, China, France, Russia and the United States, along with Germany) made a major breakthrough on April 2 in a 12-year standoff, agreeing on a framework deal.
But the sides must resolve a series of difficult technical issues, including the steps for lifting sanctions imposed on Iran, by a June 30 deadline in order to seal a final accord.
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Zarif said he thinks "we are close to a deal," but the text must still be drafted.
For an agreement to be reached, he said the "United States and some of our friends in Europe" must change their stance toward the sanctions.
Iranian President Hassan Rouhani has demanded that sanctions be immediately lifted when any deal is signed.
But the world powers have said sanctions will only be gradually eased and want a mechanism to ensure they can be swiftly reimposed if Iran breaks its word.