While the number of fighters returning home so far has been small, counterterrorism officials point to alarming signs. Three Syrian men who had traveled through Turkey and Greece were arrested by the German authorities on Tuesday on suspicion of being linked to the Islamic State operatives who attacked Paris in November, said Germany’s interior minister, Thomas de Maizière.  German security services monitored the suspects for months after they arrived in Germany in mid-November on false passports made in the “same workshop” as those of the Paris attackers, Mr. De Maiziere said.  John O. Brennan, the C.I.A. director, said at a security conference in Washington this month that while European allies had improved information sharing after the recent terrorist attacks in Paris and Brussels, many of those countries still had a “very mixed” record of progress.  United States and European officials acknowledge that they are ill equipped to thwart technologically savvy young Islamic State terrorists who use encrypted communications while they are on the move.  When fighters return to Europe, where the Islamic State operates cells in Britain, Germany, Italy, Turkey and other countries, they could link up with the existing networks and “stay below the radar” until they carry out an attack, Mr. Schoof said. Of the 260 Dutch citizens believed to have traveled to fight in Iraq and Syria, about 180 remain there, he added.  Many of the attacks conducted in Western Europe and the United States over the past six months underline the reality that returning fighters would be just one element in the Islamic State’s larger strategy to remain relevant after losing territorial control.  “Their ability to motivate troubled souls, to inspire them, remains a persistent presence in the United States,” Mr. Comey said in May.  American military officials say the battles to seize Raqqa and Mosul could be well underway within the next two or three months, flushing out thousands of foreign fighters and forcing them to make hard choices. Some may disconnect from the fight, but others will pose a threat.  “No one wants to be the last man on the ground whenever the Kurds, Iraqis or Americans arrive,” said Peter Neumann, the director of the International Center for the Study of Radicalization and Political Violence at King’s College London.  With the fighters aware that the Islamic State is no longer winning, “my prediction is that a majority will first return to Turkey, adding to instability there,” Mr. Neumann added. “Many will then try to return to their home countries. Others will move on to other conflicts.”  European countries are not the only ones that face this peril. This month, France’s defense minister, Jean-Yves Le Drian, warned that Islamic State fighters could flee to Egypt or Tunisia after being driven from their Libyan stronghold, Surt.  “They don’t disappear,” Mr. Le Drian said. “There’s a new risk that appears.”  The number of foreign terrorist fighters flowing into Iraq and Syria — once as high as 2,000 a month — has dropped to a small fraction of that figure in recent months, Western intelligence officials say, as countries crack down on potential fighters and as a shrinking Islamic State territory loses much of its appeal.  But there is another important reason the numbers are down: The Islamic State anticipated its battlefield setbacks and has adjusted accordingly. It has urged many prospective recruits in Europe and North Africa to stay put and carry out jihad at home, arguing that they are more useful as attackers and suicide bombers in their native countries.  In an audio message released on May 21, the Islamic State spokesman Abu Muhammad al-Adnani made clear that the organization would revert to its roots as a guerrilla insurgency. It was an implicit acknowledgment that the Islamic State would eventually lose its strongholds in Syria and Iraq and the very caliphate that has distinguished it from Al Qaeda and other terrorist groups.  Mr. Adnani, who until his death in a Pentagon drone strike in Syria last month also oversaw the Islamic State’s external operations, repeated his call for supporters to stay put and attack the group’s enemies wherever and however possible.  American intelligence agencies estimate that 42,000 fighters from more than 120 countries — including 260 Americans among 7,600 Westerners — have gone or tried to go to Syria and Iraq since 2011.  Estimates of how many remain in the war zone vary wildly — from 10,000 to 30,000. Turkey’s recent military operation along the Syrian border near Jarabulus closed the last major corridor that the Islamic State had been using to funnel fighters into and out of Syria.  Western intelligence and border enforcement agencies have increased their efforts to track fighters filtering out. Augmenting the efforts is a little-known, highly sensitive, American-led intelligence coordination center at a military base in Jordan, Operation Gallant Phoenix. At the base, military, counterterrorism and law enforcement agencies from several countries use publicly available software to sift through open-source information, such as social media posts, to identify possible fighters and alert their home countries.  Counterterrorism experts are divided on how many will fight to the death in Iraq and Syria, how many will try to melt back into Sunni enclaves there, and — of those seeping out — how many will pose a real threat upon going home or reaching other destinations.  “Every suicide bomber used in Manbij or Mosul or Falluja is one less foreign fighter to return,” said Andrew M. Liepman, a former deputy director at the National Counterterrorism Center who is now a senior policy analyst at the RAND Corporation.  Amarnath Amarasingam, a fellow at George Washington University’s Program on Extremism and a co-director of the study of Western foreign fighters at the University of Waterloo in Canada, said: “Amongst the hard-core, there is a threat that they will return home to launch revenge attacks as the caliphate shrinks. But there are also many fighters who will take this opportunity to disengage from the conflict entirely.”  A version of this article appears in print on September 18, 2016, on page A10 of the New York edition with the headline: Caliphate in Peril, More ISIS Fighters May Take Mayhem to Europe. Order Reprints| Today's Paper|Subscribe
The American-led coalition is closing in strongholds in Iraq and Syria But some Western officials expect consequences to that success for years to come.