House Homeland Security Committee Chair Rep. Michael McCaul, R-Texas, said on "This Week" that ISIS is waging a war against the West online, with three attacks this week against law enforcement and military personnel - two in Canada and one in the United States - serving as examples of "where they're winning."

"I think all the markings are there of radical Islamist ties," McCaul said of the attack Thursday in the New York City subway, in which an unemployed recent Muslim convert - identified by authorities as 32-year-old Zale Thompson - attacked four NYPD officers with a hatchet in broad daylight, striking one in the head before being shot and killed by police.

New York police said Friday that Thompson appears to have be picked up his Islamic extremist views himself, watching ISIS and al Qaeda videos on the Internet.

"This is the profile of the enemy within: self-radicalization within the United States," McCaul told ABC News' Martha Raddatz. "We worry a lot about ISIS traveling overseas from Syria to the United States, but I think one of the greatest fears are those already within the United States who are being radicalized and inspired by the ISIS propaganda that's out there on the Internet."

The attack came just a day after the deadly rampage in the Canadian capital when another 32-year-old Muslim convert, Michael Zehaf-Bibeau, allegedly killed a soldier who was guarding Canada's National War Memorial and then stormed the Canadian parliament building.

On Monday, another Canadian soldier was killed when his car was run off the road by a man boasting of ties to ISIS.

"They are waging a campaign of war against the West and the United States, and these are three examples just last week of where they're winning," McCaul said.

McCaul said because these homegrown violent extremists - so-called "lone wolves" - are inspired from overseas but often act alone, it is not easy to track them down.

"These are people in a basement being radicalized over the Internet," McCaul said. "They're not mentally all that sound. They're really one of the most difficult to stop. It's like finding a needle in a haystack."

But McCaul said one solution is to intervene on the local level.

"What I would urge is we have greater community involvement within the mosques," he said, noting that radical behavior noticed in a mosque should be reported to local law enforcement, who could work with the FBI.

"Remember Tamerlan Tsarnev, the Boston bomber, got literally kicked out of his mosque, and yet there was no reporting of that at that time," McCaul said. "Had there been, just maybe we could have stopped that particular bombing from happening."

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