The clerics have threatened to incite violence against him if the government caves into Western pressure and frees him.
They say they will call on people to pull him to pieces.
Abdul Rahman, 41, was jailed for converting to Christianity
and could face execution if he refused to become a Muslim again.
Afghanistan's judiciary reiterated on Thursday it would not bow to outside pressure.
Moderate Cleric Abdul Raoulf says rejecting Islam is an insult to God and the man must die.
The case of the former aid worker has ignited passions in Afghanistan and highlighted a conflict of values between the conservative Muslim nation and its Western backers.
Washington has increased pressure on Afghanistan to end the prosecution after the case angered President George W. Bush's evangelical supporters.
Secretary of State Condoleezza Rice told Afghan President Hamid Karzai by telephone that the United States wanted Afghanistan to show it respects religious freedom by resolving the case quickly.
Her call to the close US ally came a day after Bush vowed to use US leverage over Afghanistan to make sure Abdur Rahman's right to choose his religion was upheld.
According to the Canadian government, President Karzai has pledged Rahman would not be executed.
"We haven't seen a resolution to the issue, so we thought it was important to underline to the Afghan government exactly what the views of the American government, and frankly, the American people, were on this case," Dr Rice's spokesman, Sean McCormack, told reporters in explaining her call to Karzai.
US Christian conservatives, a key support base for Bush, have become increasingly vocal as the Bush administration has failed so far to have the man freed.
"It's deeply disturbing that this incident is taking place in a
country that America continues to protect and defend," the American Centre for Law and Justice, a conservative group that often focuses on Christian issues, said in a statement.
The Bush administration initially responded less forcefully than governments such as Italy and Germany.
Mr Bush first spoke in public about the case on Wednesday -just days after it won wide media attention and stirred outrage among his supporters.
State Department officials, who for days have emphasised the case was up to the Afghan government to resolve, could not say if Dr Rice raised the issue when she met the foreign minister on Monday.
Mr Bush has been criticised for reacting slowly in recent months to other controversies, such as a port management deal with a Middle Eastern company.
The case is a sensitive issue for President Karzai who depends on foreign troops to battle Taliban and al Qaeda militants, and US economic support, but also has to take balance the views of conservative proponents of Islamic law.
Death is one of the punishments stipulated by sharia, or Islamic law, for apostasy.
The legal system is based on a mix of civil and sharia law in
Afghanistan, where 99 per cent of its more than 25 million people are Muslim.
A possible compromise solution, hinted at by Afghan officials, is for the convict to avoid further punishment on the grounds he is mentally ill.
That would not satisfy the United States.
"We think that it is important for the Afghan people that this
issue of freedom of religion, freedom of expression, which is
enshrined in the Afghan constitution, be reaffirmed," McCormack said.