Ayatollah Hassan Mosafari, a member of the Assembly of Experts responsible for the election, said he was confident that a new leader would be appointed within the next 24 hours, Fars reported.
He also asked people not to spread rumours about why the election had not yet taken place.
Iran's former supreme leader, ayatollah Khamenei, was killed in an Israeli air strike on February 28, in an attack that has triggered retaliatory attacks by Iran on targets across the region.
In Iran, there has since been growing criticism in religious circles in Qom, a Shi'ite stronghold, as to why the Assembly of Experts has not yet appointed a successor although it is responsible for the process.
"We expect the Assembly of Experts to proceed swiftly on this issue in order to dash the hopes of the enemy and preserve the cohesion and unity of the nation," renowned Ayatollah Hossein Noori Hamedani said.
Influential Ayatollah Naser Makarem Shirazi also described swift implementation as the best way to strengthen Iran's sovereignty and effectively run state affairs.
Unconfirmed reports say Mojtaba Khamenei, the son of the late supreme leader, and Hassan Khomeini, the grandson of revolutionary leader Ruhollah Khomeini, are seen as the two most important candidates.
But neither Mojtaba Khamenei nor Hassan Khomeini have the rank of grand ayatollah as Iran's constitution requires.
The constitution says the Assembly of Experts, made up of 88 clerics, must appoint a new supreme leader.
Until a successor is appointed, a transitional trio led by President Masoud Pezeshkian, the head of the judiciary and another cleric are to run state affairs.
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