UNITED NATIONS—Plans were set Monday for the highest-level engagement between the U.S. and Iran in more than 30 years, fueling cautious optimism about the prospect for progress in curtailing Iran's nuclear work after a decade of threats and stalled diplomacy.

The meeting on Thursday at the U.N. General Assembly in New York will bring Iranian Foreign Minister Javad Zarif together with U.S. Secretary of State John Kerry and his counterparts from the five other major powers who are negotiating with Tehran on its nuclear program.

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