Washington (CNN) -- The U.S. government is stepping up efforts to collect intelligence on Syrian training camps and Americans returning from Syria amid concern that U.S. citizens fighting alongside extremists might later conduct attacks back home.
"The FBI and other members of the intelligence community have made this a top priority and are taking whatever steps they can under the law to monitor and prevent those coming back from doing us harm," Assistant Attorney General John Carlin said.
The increased intelligence-gathering comes during what Attorney General Eric Holder describes as a "dangerous time" for the United States.
In an interview with ABC's "This Week" on Sunday, Holder estimated there are about 7,000 foreign fighters in Syria, coming from places like Europe and the United States.
"In some ways, it's more frightening than anything I think I've seen as attorney general," he said. "This is a situation that we can see developing and the potential that I see coming up, the negative potential I see coming out of the facts in Syria and Iraq now, are quite concerning," he said.
The FBI has dozens of investigations of Americans under way in the United States as the government tries to identify potential suspects even before they travel to Syria so they know if they come back.
U.S. officials tell CNN that not all potential suspects are on the no-fly list -- making it harder for investigators to track them.
Adding to the worries: thousands of fighters in Syria with European passports who are able to enter the United States. Officials say not all European countries are sharing the names of all of their suspect citizens.
Alarms went off when a French Algerian extremist opened fire at the Jewish Museum in Brussels, Belgium, in May. After training in Syria with al Qaeda splinter group ISIS, he traveled through several countries in Europe before he was arrested in France.
U.S. officials said it was a wake-up call that borders can be readily crossed.
"We got to make sure we partner with Europe so that know who's coming back," Rep. Adam Schiff, D-California, a member of the House Intelligence Committee, told CNN's "New Day" on Tuesday. "We need to make sure that they take action against those that are providing material support to terrorism in Syria and elsewhere, because many of the European countries don't even have the laws to allow them to do that."
Meanwhile, the Transportation Security Administration said this month that security screeners at overseas airports may ask U.S.-bound passengers to turn on their cell phones and other electronics to prove they work and aren't explosive devices. The change is part of an update to security measures aimed at combating potential new threats from terrorists in the Middle East and Europe.
A senior U.S. official told CNN that part of what prompted the enhanced security measures was intelligence that militants in Syria had details on how to make undetectable bombs.
CNN's Pamela Brown, Evan Perez and Dana Ford contributed to this report.