The United States faces an increasing number of homegrown violent extremists radicalized online and inspired by jihadists in Syria to carry out acts of violence, the FBI warned Monday.

Federal Bureau of Investigation director James Comey said the danger was witnessed "in a very real way" by attacks that killed two soldiers in Canada in recent weeks.

In a speech in New York, Comey said tracking down those inspired by the so-called Islamic State group in Syria was "extremely difficult and something we spend every single day working on."

The risk is nationwide and is represented by people of all ages, different ethnic backgrounds and all walks of life, he told a conference on counter-terrorism at Fordham Law School.

"It's a problem wherever there are troubled souls with access to the Internet and that is everywhere in this great country of ours."

Without meeting a member of Al-Qaeda, they are radicalized by online propaganda and are "equipped to engage in their jihad without ever actually leaving their basement or bedroom," he said.

"(They) can get all they need on the Internet to engage in an act of violence here in the United States," he said, urging Americans to report any suspicious change of behavior they may notice.

"Given the complexity of the threats we face, the diversity of the forces overseas and the explosion of opportunities for homegrown violent extremists our safety has to be a collective effort."

"If you don't say something, we all may regret it that you didn't listen to the hair on the back of your neck," he said.

Comey has estimated that about a dozen Americans are fighting with terror organizations.

"We track them very carefully if they're coming back to the United States. If I have evidence that you have fought with any of these foreign terrorist organizations you will be locked up," he said.

The FBI director also warned again that moves from Apple and Google to encrypt all customers' data would make it harder to track down those using social media to plot terror attacks.

"There should be no one in the United States above the law and... also no places within the United States that are beyond the law," he said, calling for greater debate on liberty and security.