The previously announced two-day meeting comes after fruitless talks between Iran and world powers in Vienna earlier this month when no "tangible progress" was made ahead of a July 20 deadline for a comprehensive agreement.
"The meeting has begun at Istanbul's Ciragan Palace," an Iranian diplomat told AFP on condition of anonomity.
The diplomat insisted that the future of the talks depended on the willingness of both parties. "At the moment it is not yet certain," he said.
The tete-a-tete would be followed by a dinner at the Iranian consulate, he said.
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ISNA news agency, citing a source close to the Islamic republic's nuclear team, reported that Zarif was being accompanied on the trip by senior members of his nuclear negotiations team.
Speaking to the official IRNA news agency prior to his departure, the foreign minister reiterated that snags along the way to a conclusive deal "may be part of negotiation tactics," but differences should be hammered out at the table.
No further details of the discussions with Ashton in Istanbul were disclosed but the last round of talks in Vienna proved that major issues remain.
These reportedly include the scope of Iran's enrichment of uranium, which if further purified could be used to make a nuclear weapon, and its unfinished Arak research reactor, whose by-product waste could provide an alternative route to an atomic bomb.
Iranian and Western negotiators spoke of major gaps between the two sides at the Vienna talks. The differences prevented a start being made on an early draft agreement.
But all sides have since expressed a willingness to continue the talks.
The P5+1 is seeking to curb Iran's disputed nuclear activities. International monitors suspect Tehran could be masking military objectives.