TEHRAN, Aug. 12 -- For five months after U.S. and Israeli strikes hit Tehran and upended Iran's succession, Mojtaba Khamenei ran the country from somewhere that wasn't on television. On Sunday, he appeared on it.

The new Supreme Leader met with President Masoud Pezeshkian, according to a statement distributed on Telegram, marking his first public appearance since the start of what he has called the "Third Imposed War" against Iran. A video of the meeting circulated separately from the statement. The specific timing and location of the encounter were not disclosed.

What was discussed, according to the statement, covered three areas: the Iranian rial, energy policy, and military matters. None of those categories is small. The rial has los...