"Confrontation with the U.S. is not a value by itself, " Qalibaf said.

NPR: Next Iran President Likely To Have Gentler Touch

They include the country's main nuclear negotiator, Saeed Jalili, former nuclear negotiator Hassan Rohani, former foreign minister Ali Akbar Velayati, and the mayor of Tehran, Mohammad Baqer Qalibaf.

BBC: Rafsanjani and Mashaei barred from Iran presidency poll

Velayati has deferred to Khamenei on any possible overtures to the U.S. But Qalibaf and others suggest they would urge the leadership to remain open for direct talks.

NPR: Next Iran President Likely To Have Gentler Touch