The Afghan government says it is up to the judiciary to decide the fate of a man who could face death for converting to Christianity.
Questions are being asked about Mr Rahman's mental health
Abdul Rahman, 41, is charged with rejecting Islam and could be executed under Sharia law unless he reconverts.
But prosecutors, echoing earlier comments by the judge, said questions had been raised about whether he was mentally fit to stand trial.
The US and three Nato allies have expressed concern over the case.
US President Bush said on Wednesday he was "deeply troubled" about the case.
Mr Bush made his remarks in a speech defending his decision to go to war in Afghanistan and Iraq. He called on the Afghan government to allow Mr Rahman to worship as he chose.
The Afghan government says it is up to the courts to decide the matter.
Khaleeq Ahmed, deputy spokesman for Afghan President Hamid Karzai said: "The judicial system is an independent system.
"This is a case that the family of the person brought against him. We are watching it closely and Afghanistan also respects human rights."
'I am not an infidel'
Mr Rahman converted 16 years ago as an aid worker helping refugees in Pakistan. His estranged family denounced him during a custody dispute over his two children.
His mental health was questioned by the judge earlier in the week and on Thursday prosecutor Sarinwal Zamari said there were doubts about whether he was fit to stand trial under Sharia law.
He told the Associated Press: "We think he could be mad. He is not a normal person. He doesn't talk like a normal person."
But Mr Rahman told the court: "They want to sentence me to death and I accept it, but I am not a deserter and not an infidel. I am a Christian which means I believe in the Trinity."
The US made a subdued appeal for him to be allowed to practise his faith - but stressed it did not want to interfere.
Germany, Italy and Canada, which all have troops in Afghanistan, also voiced concern over Mr Rahman's plight.
The Italian foreign ministry said Mr Rahman's plight was incompatible with the defence of human rights and fundamental freedoms.
The chairman of the German Bishops' Conference, Cardinal Karl Lehmann, said the case sent an "alarming signal" about freedom of worship in Afghanistan.
Canada has called on Afghanistan to meet its human rights obligations.
Observers say executing a converted Christian would be a significant precedent as a conservative interpretation of Sharia law in Afghanistan.
Mr Rahman's is thought to be Afghanistan's first such trial, reflecting tensions between conservative clerics and reformists.
Conservatives still dominate the Afghan judiciary, four years after the Taleban were overthrown, and Afghanistan's post-Taleban constitution is based on Sharia law.
US President George Bush only recently visited Kabul, praising the country's emergence from years of oppression under the Taleban.