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Paris • The Paris attackers exploited intelligence holes from France to Syria, authorities say, taking advantage of mistrust between European governments, France's overwhelmed security services and the collapse of authority across the war zone contested by the Islamic State.

Eleven days after the attacks, French authorities have announced few details about the investigation, and Brussels remains locked down for reasons the government has hardly explained. Officials and security experts say it seems clear that Europe's borderless travel and suspicion between governments at sharing intelligence information left the continent vulnerable.

"Dealing with just the sheer number of foreign fighters, of known and potential terrorists in a country like France, has without question started to overwhelm the French security services," Christopher S. Chivvis, associate director of RAND's International Security and Defense Policy Center, told The Associated Press.

On the European level, he said, mistrust between intelligence agencies, as well as privacy concerns, have complicated how the bloc is policed: "Unless the will is there to actually share intelligence between one agency and another, it's just not going to happen."

As many as four attackers' remains have not been publicly or fully identified, including two with questionable Syrian passports. The total number of attackers has not been spelled out, and French authorities have not said how many people directly involved could still be at large. These gaps point to a security service that was caught off guard.

The head of Frontex, Europe's border-control agency, conceded that lack of European cooperation is a grave issue, saying the agency conducts no security checks on its own because European governments don't trust each other enough to pool databases.

"We are paying today for this lack of trust, which has lasted a decade," Fabrice Leggeri, the Frontex chief, told Le Parisien newspaper.

President Barack Obama cautioned Tuesday against speculation on what went wrong before the Paris attacks. But he underscored the need for better information sharing: "What is true is we can do a better job of coordinating between countries," Obama said in a joint White House news conference with French President Francois Hollande.

Authorities have not yet pinpointed the role of the suspected mastermind, Abdelhamid Abaaoud, nor the lone fugitive in the attacks, Salah Abdeslam. Nor have they explained why — nearly 12 hours after the assault began — a gendarme near the Belgian border stopped, then released Abdeslam, whose brother was among the suicide bombers and whose rental car had already been linked to the attack.

Salah Abdeslam is still on the run. Left behind was an unexploded suicide vest found in the trash Monday in the same suburb where his cellphone pinged the night of the attacks, according to the French officials.

Two of the suicide attackers at France's national stadium had Syrian passports that officials believe to be fakes. Both were recorded passing through the Mediterranean island of Leros on Oct. 3, Greek officials say.

France's Interior Minister Bernard Cazeneuve said the attacks "were prepared by cells outside our borders using people who were not known to our intelligence services."

Two U.S. officials said many — though not all — of the attackers identified were on the U.S. no-fly list. All but one of those identified in the attacks are French, and many have deep ties to Belgium. The majority are believed to have come home after training with Islamic extremists in Syria, as have more than 500 French extremists — more than any other Western European country.

The senior American official said the U.S. has seen nothing suggesting European intelligence services missed a crucial piece of information that should have led to the disruption of the plot. But he said they appeared to have been unable to put the disparate strands together fast enough to stop the attack, which was planned in large part via encryption. He said the French were simply overwhelmed by the number of radicals in their midst.

One French police official, with knowledge of the investigation, said it came as a surprise to learn that Abaaoud, the suspected mastermind, had a cousin in the Paris suburb of St. Denis who was already under investigation in a drug case. The official said it was even more of a shock to learn that Abaaoud himself was in the same Paris area, despite his status as one of Europe's most wanted men. Abaaoud is among the dead in the rubble of a St. Denis home that was raided on Nov. 18.