A picture taken from the Turkish border near the southeastern village of Mursitpinar, in the province of Sanliurfa, shows smoke billowing after a fighter jet hit Kobane in Syria.

Oct. 28, 2014 A picture taken from the Turkish border near the southeastern village of Mursitpinar, in the province of Sanliurfa, shows smoke billowing after a fighter jet hit Kobane in Syria. AFP/Getty Images

The United States has stepped up airstrikes against Islamic State forces massed around the Syrian town, and Kurdish forces say the militants’ offensive has stalled.

The United States has stepped up airstrikes against Islamic State forces massed around the Syrian town, and Kurdish forces say the militants’ offensive has stalled.

More than 1,000 foreign fighters are streaming into Syria each month, a rate that has so far been unchanged by airstrikes against the Islamic State and efforts by other countries to stem the flow of departures, according to U.S. intelligence and counterterrorism officials.

The magnitude of the ongoing migration suggests that the U.S.-led air campaign has neither deterred significant numbers of militants from traveling to the region nor triggered such outrage that even more are flocking to the fight because of American intervention.

“The flow of fighters making their way to Syria remains constant, so the overall number continues to rise,” a U.S. intelligence official said. U.S. officials cautioned, however, that there is a lag in the intelligence being examined by the CIA and other spy agencies, meaning it could be weeks before a change becomes apparent.

The trend line established over the past year would mean that the total number of foreign fighters in Syria exceeds 16,000, and the pace eclipses that of any comparable conflict in recent decades, including the 1980s war in Afghanistan.

U.S. officials have attributed the flows to a range of factors, including the sophisticated recruiting campaigns orchestrated by groups in Syria such as the Islamic State and the relative ease with which militants from the Middle East, North Africa and Europe can make their way to that country.

View Graphic Map: Flow of foreign fighters to Syria

American officials stressed that the stability of the flow is not seen as a measure of the effectiveness of an air campaign that expanded beyond Iraq and into Syria late last month. The latest estimates indicate that strikes in Syria alone have killed about 460 members of the Islamic State — the group that has beheaded two American journalists and two British aid workers — as well as about 60 fighters from Jabhat al-Nusra, an al-Qaeda affiliate.

The United States and its allies have carried out more than 600 strikes so far in Syria and Iraq, bombings aimed primarily at slowing the Islamic State’s advances and allowing the Iraqi military and moderate opposition forces in Syria to regroup. Rear Adm. John Kirby, spokesman for the Pentagon, said this week that the strikes are “disrupting” the Islamic State’s operations but acknowledged that any major offensive against the group “may still be a ways off.”

Experts said the foreign fighter population is likely to grow significantly larger as the three-year-old conflict drags on.

“I don’t think 15,000 really scratches the surface yet,” said Andrew Liepman, a counterterrorism expert at Rand Corp. who formerly was the deputy director of the National Counterterrorism Center.

Since the start of the U.S.-led air campaign, analysts have sought to track whether the bombings would discourage would-be fighters or serve as a rallying cry for Islamists. Liepman said the steady numbers could mean that neither has occurred or, more likely, that both have happened to degrees that offset one another.

The air campaign “has probably discouraged some people and encouraged others,” Liepman said.

He and others cautioned, however, that there are significant gaps in U.S. intelligence on the conflict in Syria, making it difficult to have a clear understanding of the scale and composition of the swelling population of foreign fighters.

The vast majority of those militants have come from other countries in the Middle East and North Africa. Tunisia has sent more fighters to Syria than any other nation.

More than 2,000 fighters have come from countries in Europe, carrying passports that would enable them to travel relatively freely in Western countries.

Many went to fight the government of Syrian President Bashar al-Assad and may pose no security threat beyond that country’s civil war. But security officials have expressed mounting concern over more recent arrivals who have fought with the Islamic State or al-Nusra, which has a cell near Aleppo that was established to plot attacks against Western nations.

Britain, France, Germany and other European nations have taken increasingly aggressive measures over the past year to stem the flow of fighters to Syria, seizing passports, passing new antiterrorism measures and targeting suspects with stepped-up surveillance and arrests. U.S. officials have said that about 130 Americans have traveled to Syria or tried to do so.

Most militants entering Syria have done so through Turkey, a country that has recently sought to tighten control over its borders and root out Islamist networks that serve as pipelines for fighter.

U.S. officials said it could be too soon to see clear indications that such measures are working.

“The Europeans and other allies are taking steps upstream to stem the flow of their citizens to Syria, while at the downstream end, the Turks are taking action to keep their borders from being exploited by jihadists,” the U.S. intelligence official said. “It could take some time for the dampening effect of these measures to start showing up in the foreign-fighter intelligence estimates.”

Although U.S. officials have not made public estimates of the rate at which foreign fighters are flowing into Syria, they have provided totals that trace a clear trajectory. The 15,000 figure cited by the White House last month was up sharply from an estimate of 12,000 in July and 7,000 in March.

Missy Ryan contributed to this report.