FBI Director James Comey predicted an exodus of Islamic State fighters spreading worldwide as they prepare for the potential fall of the so-called caliphate in Iraq and Syria, warning lawmakers Thursday that ISIS will become increasingly “desperate” to launch attacks elsewhere.

During a hearing before the House Homeland Security Committee, Comey and other top security officials also acknowledged concerns over ISIS operatives using fraudulent documents to gain entry into western countries.

Homeland Security Secretary Jeh Johnson noted there is "general concern" over the issue.

Comey repeatedly stressed the U.S. and its allies must stay vigilant, as ISIS moves its focus away from the Iraq and Syria battlefield, and operatives spread out.

“We all know, there will be a terrorist diaspora out of the caliphate as military force crushes the caliphate,” Comey said. “Those thousands of fighters are going to go someplace. Our job is to spot them and stop them before they come to the United States to harm innocent people.”

Comey essentially echoed a warning delivered last month by CIA Director John Brennan , who warned that U.S.-led efforts to strike at the terror group have not hampered its “terrorism capability and global reach.” Brennan had said ISIS likely will “intensify” terror attacks around the world even as its core fighters come under pressure in Iraq and Syria.

On that point, Comey told lawmakers on Thursday, “As the caliphate is crushed, the so-called Islamic State will become more desperate to demonstrate its continued vitality, and that will likely [take] the form of more asymmetric attacks, more efforts at terrorism.”

He said “we can't take our eye off of what the next move will be by these killers.”

Battlefield gains against ISIS are fueling the warnings that global attacks will rise – amid a wave of recent attacks.

The Washington Post reported Tuesday that the terror group’s leaders in Syria are bracing for its strongholds to fall, but vow to continue its wave of terror attacks abroad. U.S. counterterrorism experts believe the recent large-scale attacks in Istanbul and Baghdad are a sign that its reign in the Middle East is dwindling.

House Homeland Security Committee Chairman Michael McCaul, R-Texas, who cited a prior “diaspora” prediction by Comey in his opening remarks, called the attacks and plots connected to ISIS since 2014 an “unprecedented wave of terror.”

“I’m concerned that we have only seen the tip of the iceberg,” McCaul said, adding that the “exodus has now begun” of jihadists returning home.

Comey also noted a decline in the number of travelers leaving the U.S. to join ISIS. As he has in past remarks, Comey said he hopes the decline is a function of individuals seeing the "mirage" that is the so-called Islamic State.

Comey did note, however, that the decline could very well be a result of individuals wanting to stay at home to commit violence.

Fox News’ Matthew Dean contributed to this report.