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Dozens of people in the U.S. are engaged in conversations with overseas supporters of ISIS that the FBI cannot monitor, FBI Director James Comey said Thursday.

He has been warning for months that when ISIS supporters find someone in the U.S., through messages on social media, they then employ software that encrypts their communications, making it impossible for the FBI to follow them, even with a court order.

"ISIS is sending a poisonous message that buzzes in the pockets of troubled souls, unmoored people, all day long," Comey told the Senate Homeland Security Committee. "The challenge we face is finding those needles in a nationwide haystack, assessing where they are on a spectrum between consuming this poison and acting on it, and disrupting them before they act."

When ISIS recruiters find "a live one," he said, "they move to end-to-end encryption, so the needle we have found disappears on us once it becomes most dangerous."

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While Comey has discussed the "going dark" challenge before, his comments Thursday represent the first time he has put a number on the size of the problem.

Related: U.S. Doing Too Little to Stop Foreign Fighters: House Homeland Security Report

He said conversations with the technology industry are promising, searching for a way to allow the government, with a court order, to monitor those communications.

The director of the National Counterterrorism Center, Nicholas Rasmussen, said 28,000 people have traveled to areas controlled by ISIS over the past three years, including 5,000 from western countries and 250 from the United States.

Several senators expressed concern that terrorists could be among Syrian refugees seeking to come to the U.S.

"We have to be careful about doing it. There's no such thing as a risk-free enterprise," Comey said.

Homeland Secretary Secretary Jeh Johnson said the government's ability to screen potential refugees has improved. He said the process begins when the UN's refugee agency informs the federal government of people seeking to come here who have family members living in the U.S.

Representatives of the State Department and U.S. Citizenship and Immigration Services will meet with refugees and interview them, and their names will be checked against law enforcement and intelligence databases.

"But this is a population of people that we're not going to know a whole lot about," Johnson said.