WASHINGTON - With the criminal investigation of the Sept. 11 attacks increasingly focused on several European countries, U.S. authorities are using diplomacy as much as detective work to build cases and persuade other nations to hand over key suspects for prosecution in the United States.

Attorney General John Ashcroft began a four-day visit yesterday, hoping to ease European concerns about handing over suspected terrorists who could face the death penalty or trial by U.S. military tribunal. Most U.S. allies oppose both options.

At a London news conference, Ashcroft promised that questions of extradition and punishment would be dealt with "on a case-by-case basis." He was careful to say that each country must decide on its own how best to fight terror.

"Each nation has to make its own judgments about those things that it can and needs to do to protect its innocent citizens from being the victims of savage terrorist attacks," Ashcroft said.

Even with such assurances, foreign policy analysts say, Ashcroft is unlikely to easily erase concerns among countries such as Britain, France and Spain, which have arrested suspected terrorists. Those nations refuse to extradite suspects without guarantees that defendants would not face the death penalty, either in federal courts or military tribunals. A European Union charter adopted last year bars extradition to nations where a suspect could face the death penalty.

Ashcroft "is not going to convince the European Union to change their position on the death penalty," said Ivo H. Daalder, a European affairs adviser on President Bill Clinton's National Security Council and now a senior fellow at the Brookings Institution. "In my opinion, there is room for give in only one direction - we change our position."

That seemed true this week as several European leaders raised fresh objections to the U.S. death penalty. In France, Justice Minister Marylise Lebranchu said her country would oppose the death penalty for Zacarias Moussaoui, a French citizen who this week became the first person to be indicted by the United States on charges directly related to the September attacks.

Before Ashcroft arrived in London to begin the European tour that will also take him to Spain, Germany and Italy, British Defense Secretary Geoff Hoon indicated that even if suspected terrorist mastermind Osama bin Laden turns up on British soil, he would be extradited to the United States only if he would not face the death penalty.

Prime Minister Tony Blair played down Hoon's remark, saying that British troops would automatically turn bin Laden over to the United States if they captured him.

Ashcroft, traveling with top officials from the Justice Department, the FBI and the Drug Enforcement Administration, praised European investigators for sharing intelligence and helping track leads during the first three months of the investigation.

"All of the investigative leads we have asked our British colleagues to track down, particularly in the identification of emerging threats, have been expertly and relentlessly pursued," Ashcroft said. "We are grateful."

Authorities say they believe that much of the planning for the Sept. 11 attacks was carried out by a terrorist cell operating in Hamburg, Germany. Moussaoui, who officials suspect was recruited to be the 20th hijacker, came to the United States in February from London, where he had lived during the 1990s and where relatives have said he became increasingly radical.

German prosecutors have issued arrest warrants for three men believed to have been directly involved in planning the attacks. The Justice Department said this week that one of those fugitives, Ramsi bin al-Shibh, is thought to be in Afghanistan.

The United States has sought extradition in only one European terror case, and in that instance is not seeking the death penalty.

Lofti Raissi, a 27-year-old Algerian pilot being held in London, was indicted in Arizona on charges of lying to federal agencies on a U.S. pilot's application. In arguing for Raissi's return to the United States, a U.S. prosecutor argued that Raissi had helped another Algerian terror suspect obtain false immigration papers and was suspected of being linked to a bomb plot at Los Angeles International Airport.

A British judge has refused the extradition request, saying the evidence against Raissi represents, at best, "a tenuous connection" to the September attacks.

In Spain, authorities have arrested 14 suspected members of the al-Qaida terrorist network, but officials have expressed concerns that the men, if turned over to the United States, could face trial before military tribunals - without many of the constitutional protections afforded in federal court.

The Justice Department's decision to try Moussaoui in federal court could reinforce Bush administration assertions that such tribunals would be used only in limited cases, perhaps only against al-Qaida leaders.

"This is an illustration of how carefully the president plans to employ this tool he has created," William J. Haynes II, a Defense Department lawyer, said at a Senate Armed Services Committee hearing yesterday.

In announcing Moussaoui's indictment Tuesday, Ashcroft declined to say whether prosecutors would seek the death penalty.

Lebranchu, the French justice official, said the United States should remain open on that question.

"There has to be a discussion with the United States," Lebranchu said yesterday on RMC-Info Radio in France. "We do not accept the death penalty."