Muslim clerics condemned Abdul Rahan's release, saying it was a "betrayal of Islam" and threatened to incite violent protests.
The 41-year-old was released from the high-security Policharki prison on the outskirts of Kabul late Monday after a court dropped charges of apostasy against him because of a lack of evidence and suspected mental illness.
Justice Minister Mohammed Sarwar Danish said Rahman was staying at a "safe location" in Kabul.
Rahman has appealed to leave Afghanistan and the United Nations said it has been working to find a country willing to take him.
The Italian government said in a statement that Foreign Minister Gianfranco Fini will use a Cabinet meeting Wednesday to press for Rahman to be granted asylum there.
Fini had earlier expressed Italy's "indignation" over the case. Pope Benedict XVI also appealed to Karzai to protect Rahman.
Italy has close ties with Afghanistan, whose former king, Mohammed Zaher Shah, was allowed to live with his family in exile in Rome for 30 years. The former royals returned to Kabul after the fall of the Taliban regime in 2001.
An Italian diplomat in Kabul, who spoke on condition of anonymity because of the sensitivity of the matter, said no one from the Italian mission had been in contact with Rahman, but they had been assured his health was all right.
Rahman was arrested last month after police discovered him with a Bible during a custody dispute over his two daughters. He was put on trial last week for converting 16 years ago while he was a medical aid worker for an international Christian group helping Afghan refugees in Pakistan. He faced the death penalty under Afghanistan's Islamic laws.
Deputy Attorney-General Mohammed Eshak Aloko said prosecutors had issued a letter calling for Rahman's release because "he was mentally unfit to stand trial."
"We had to give them evidence that yes, he was mentally sick and he has to want treatment," Sahmee Sahma, of the Afghan government-appointed Human Rights Commission in Kabul, told CBS News.
Aloko also said he did not know where Rahman had gone after being released. He is likely heading out of Afghanistan since his life would be in jeopardy on the streets of Kabul, CBS News correspondent Tom Coughlin reports.
He said Rahman may be sent overseas for medical treatment.
CBS News correspondent Sheila MacVicar quotes one investigator as saying the testimony included a statement from Rahman's daughter, saying that he has mental problems.
The case set off an outcry in the United States and other nations that helped oust the hard-line Taliban regime in late 2001 and provide aid and military support for Afghan President Hamid Karzai. U.S. President George W. Bush and others had insisted Afghanistan protect personal beliefs.
But the outrage put Karzai in a difficult position because he also risked offending religious sensibilities in Afghanistan, where senior Muslim clerics have been united in calling for Rahman to be executed.
"This is a betrayal of Islam and the entire Afghan nation by our government," said Hamiddullah, a senior cleric in Kabul. "This will have very dangerous consequences for the government. Muslim leaders will react very strongly."
A cleric in northern Kunduz town, Ubuiddullah, said, "We will protest this. We are very angry."
A preacher, though, in northwestern Badghis province said the country's religious leaders shouldn't incite violence.
"Clerics shouldn't be calling for people to riot and damage our country," Mohammed Usman said.
About 700 clerics, students and others protested Monday in the northern city of Mazar-e-Sharif over Rahman's acquittal. The demonstration ended peacefully and there has been no other rally since.