Those two approaches seem to have collided in the case of an Egyptian cleric, Hassan Mustafa Osama Nasr, or Abu Omar, who led a militant mosque in Milan.

By early 2003, the Italian secret police were aggressively pursuing a criminal terrorism case against Mr. Nasr, with the help of American intelligence officials. Italian investigators said they had told the Americans they had strong evidence that he was trying to build a terror recruitment network, possibly aimed for Iraq if the United States went forward with plans to topple Saddam Hussein.

On Feb. 17, 2003, Mr. Nasr disappeared.

When the Italians began investigating, they said, they were startled to find evidence that some of the C.I.A. officers who had been helping them investigate Mr. Nasr were involved in his abduction.

"We do feel quite betrayed that this operation was carried out in our city," a senior Italian investigator said. "We supplied them information about Abu Omar, and then they used that information against us, undermining an entire operation against his terrorist network."

He and other senior Italian officials in Milan's police and prosecutor's office were angry enough to answer detailed questions about the case, but insisted on anonymity because the investigation is continuing.

"This whole investigation has been very difficult because we've been using the same methods we used against organized crime to trace the activities of people we considered to be our friends and colleagues," the senior Italian investigator said. "It has been quite a troubling affair."

The Italian warrants - requested by Milanese prosecutors after two years of investigations - accuse 13 people identified as American C.I.A. officers and operatives of illegally abducting Mr. Nasr from a Milan street and flying him to Egypt for questioning. The whereabouts of the 13 are unknown, but the charges are criminal. If convicted, they face a maximum penalty of 10 years and 8 months in prison.

The C.I.A. has declined to comment, and officials at the American consulate in Milan and the American Embassy in Rome have also declined to talk about the case.

The Italian police and prosecutors said the C.I.A.'s top official at the United States consulate in Milan, a man accused in the arrest warrant of coordinating Mr. Nasr's abduction, had been in close contact with them as they pursued intensive investigations into Al Qaeda and other Islamic militant networks in Europe.

Italian investigators said they were surprised when they discovered that he had placed a cellphone call to one of their own police officers not long after Mr. Nasr disappeared, but made no mention of what had happened, they said. The frustration expressed by the Italians echoes similar sentiments among some counterterrorism officials in other European countries.

In addition to their objections to the American rendition policy, European counterterrorism officials also partly blame a lack of access to terrorism suspects and information held by the United States for their failure to convict a number of their own high-profile terrorism suspects.

"The American system is of little use to us," a senior Italian counterterrorism investigator said. "It's a one-way street. We give them what we have, but we are given no useful information that can help us prosecute people."

Sharing access has become a sore point between American and European officials in several high-profile terrorism cases in Europe, including that of Mounir el-Motassadeq, a suspected associate of several Sept. 11 hijackers. On Feb. 19, 2003, he was convicted in Germany on charges related to the 2001 attacks - the only conviction thus far - but the case crumbled on appeal, and he was released in April 2004. German officials openly blamed American officials for failing to provide crucial evidence. He is being retried.

And the Bush administration has refused to allow the Spanish authorities to interview Ramzi bin al-Shibh, a central Qaeda suspect, to bolster their case against two men on trial in Madrid on charges of helping to plan the 2001 attacks.

The rockiness in the relationship between the Italians and the Americans is a relatively new development in the two countries' counterterrorism efforts. Beginning in 1998, the Italian police had worked closely with the F.B.I. in tracing the Egyptian militant group Gamaa Islamiya within Europe when the two agencies jointly monitored the telephones of a crucial operative based in Milan, officials said.

After the Sept. 11 attacks, several F.B.I. agents arrived in Milan and established a close working relationship with the secret police, officials said.

As early as spring 2002, the Italians tipped off the Americans about Mr. Nasr's activities, Italian investigators said. Methodically, using a mixture of electronic surveillance, wiretaps and surveillance, the Italian police collected evidence that Mr. Nasr was trying to build a jihadist recruitment network with tentacles spreading throughout Europe.

The police and investigators said they had evidence that Mr. Nasr's anti-American speeches and calls to jihad were resonating with young Muslim men who were attending his Islamic center here. Secret listening devices had been placed in Mr. Nasr's home and inside several mosques, officials said.

According to court records, this exchange occurred in one eavesdropped conversation at a Milan mosque, recorded by the Italian secret police:

Unidentified speaker: "We must find money because our objective is to form an Islamic army, which will be known as Force 9."

Mr. Nasr: "How are things going in Germany?"

Unidentified speaker: "We can't complain. There are already 10 of us, and we are also concentrating our efforts on Belgium, Spain, the Netherlands, Egypt and Turkey. But the hub of the organization remains London."

The Italian investigators shared a transcript of this conversation and others with the Americans, who were growing more concerned about Mr. Nasr's openly militant remarks, investigators said.

At first, the Italian investigators said they had suspected that Mr. Nasr was kidnapped by the Egyptians, possibly with the complicity of some Italian authorities.

"It's a serious breach of Italian law; it's absolutely illegal," said Armando Spataro, Milan's deputy chief prosecutor who led the investigation of Mr. Nasr and the kidnapping inquiry.

Mr. Spataro said he and his colleagues were determined to investigate the kidnapping like any other crime by the book.

It took more than two years, but all the evidence - including cellphone use and the timing of the American officials' arrival and their movements - led the Italians to conclude the kidnapping operation was conducted by the 13 Americans, with the help of six other C.I.A. officials who are still under criminal investigation, they said. Mr. Spataro applied for the arrest warrants in March, and they were signed this week by Judge Chiara Nobili.

Some former American intelligence officials said in interviews that there might be political motivations behind the warrants. On Saturday, Mr. Spataro declined to comment on any accusations of political bias.

But an Italian judicial official pointed out that Mr. Spataro, 56, is not a member of any political party. He faced accusations of right-wing bias when he led prosecutions of the Red Brigade terrorist organization in the late 1970's and 1980's. Two of his colleagues, the official said, were killed by the Red Brigades.

"I think people in Washington may not understand that in Italy a prosecutor does not choose what to investigate," the official said. "He has a legal obligation to investigate any crime."

Mr. Spataro, in a recent interview, expressed his disdain for the Americans' use of rendition, though he denied that he was motivated by that when he asked a judge to sign the arrest warrants against the C.I.A. officials. "I feel the international community must struggle against terrorism and international terrorist groups in accordance with international laws and the rights of the defendant," he said. "Otherwise, we are giving victory to the terrorists."

The warrant documents, obtained by The New York Times, describe in detail how Mr. Nasr was flown through Germany to Egypt, where he told his family and friends, during phone calls in April 2004, that he was subjected to electroshock treatment and that he had lost the hearing in one ear.

The Italians said their anger and disappointment with the Americans did not end there. They said that when they later asked the Americans about Mr. Nasr's whereabouts, they were told that American intelligence had discovered that he had surfaced somewhere in the Balkans.

On Monday, Judge Nobili is expected to appoint public defenders to represent each of the accused C.I.A. officers and operatives. Under the Italian legal system, it is normal to appoint lawyers for accused criminals, even before they have requested legal assistance.

Once these lawyers are appointed, the judge's 230-page arrest warrant, which includes a full investigative report and the names and personal details of the accused, will become public. Warrants for the arrest of the 13 C.I.A. agents will also be passed on to Interpol, effectively requiring countries around the world to assist the Italian investigation."