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The director of the Federal Bureau of Investigation said investigators have been stymied by Islamic State’s use of encryption.

FBI Director James Comey, speaking at a cybersecurity conference Wednesday at the Federal Reserve Bank of New York, said the bureau has tracked Islamic State recruiting efforts on Twitter and reviewed private messages between sympathizers after obtaining court orders.

But when Islamic State commanders find a recruit willing to die for the cause, they move their communications over to encrypted platforms, “going dark,” he said.

Mr. Comey didn’t say whether encryption was used in planning or executing the Paris attacks, but the massacre loomed large at the conference, which included law-enforcement officials from the U.S., U.K. and France.

His remarks were part of a public campaign by law-enforcement and intelligence officials for access to encrypted phones and communications, in the face of new software and devices promoted by companies as impervious to government surveillance.

The aftermath of the Paris attacks could bolster the argument in favor of such access after years of​ movement toward more customer privacy, fueled by revelations of U.S. surveillance programs.

U.S. counterterrorism officials haven’t determined whether terrorists used encrypted communications to plan or execute the Paris attacks, but they said they expect evidence to emerge as the investigation continues.

Sen. Richard Burr (R., N.C.), chairman of the U.S. Senate Intelligence Committee, said after a briefing by senior intelligence officials Tuesday that the terrorists involved in the Paris attacks likely used “end-to-end” encryption. He said encryption was likely because no direct communication among the terrorists was detected.

Islamic State, which claimed credit for the bloodshed, has demonstrated its technological savvy in tutorials for sympathizers on how to evade electronic surveillance on the cheap, including an eight-minute video explaining the eavesdropping capabilities of hostile governments and how they track phones.

Other Islamic State bulletins ​have analyzed the vulnerabilities of brands of electronic equipment and messaging applications, ranking them based on their ability to foil surveillance.

In separate remarks Wednesday, Manhattan District Attorney Cyrus Vance ​Jr.. said his office has been unable to access evidence on encrypted phones in 111 cases handled by his office. Newer operating systems on phones made by Apple Inc. and Google can’t be unlocked without the user passcode, even by the companies themselves.

Mr. Vance called for legislation that would mandate that mobile-phone companies have the capacity to unlock a customer device when presented with a search warrant. “We don’t want a key held by the government,” Mr. Vance said.

Neema Singh Guliani, legislative counsel for the American Civil Liberties Union, called Mr. Vance’s proposal “misguided” and disputed assertions that encrypted devices have undermined law enforcement.

The law advocated by Mr. Vance would “compromise the security of Americans by making their personal information and communications more vulnerable to cyberattack and theft,” she said.