Abdul Rahman, 40, was detained earlier this month for rejecting Islam and may face the death penalty, although the signs are that the authorities are looking for a way quietly to drop the case.
The case has raised protests in the West, threatening to create a rift between Afghanistan and the US and other Western backers who have called for the man's release.
"America stop interference, [President] Karzai enforce justice, he should be punished," one cleric told the crowd.
Security forces surrounded the protesters but did not intervene.
The religious leaders called for protests across the country against the government and the West.
Earlier on Monday, a prosecutor said the case against Abdul Rahman depended on the result of a mental examination.
The prosecutor, Zemarai, who uses only one name, declined to give details of the examination but said it would take place on Monday.
A spokesman for the Supreme Court had earlier stated that checks were also necessary to see if Abdul Rahman had a second nationality. He did not elaborate.
Analysts expect the case to be dropped if Abdul Rahman is found to be unstable.
Abdul Rahman told a preliminary hearing two weeks ago that he had become a Christian while working for an aid group helping Afghan refugees in Pakistan, 15 years ago. He has denied that he is mentally unstable.
"America stop interference, Karzai enforce justice, he should be punished"
Cleric in the protest
Death is the punishment stipulated by the Islamic sharia law for apostasy. The Afghan legal system is based on a mix of civil and Sharia law.
According to the Afghan constitution, "no law can be contrary to the sacred religion of Islam". But the constitution also states that Afghanistan will abide by international agreements, including the Universal Declaration of Human Rights, which enshrines freedom of religion.
The government has been searching for a way out of the problem, trying to satisfy Western demands while not angering Afghanistan's powerful conservatives, who have stated that they will "consider struggle their legal and religious duty" if Islamic law is not enforced in this case.