The Federal Bureau of Investigation told law-enforcement agencies around the country Friday it would try to help them open locked phones or other devices as much as “legal and policy constraints’’ allow.

The unusual guidance from the nation’s premier law-enforcement agency is in response to a surge of interest from state and local authorities in how the FBI was able to open a locked iPhone seized in the probe of a terror attack in San Bernardino, Calif., in December.

The FBI advisory seems to be aimed at reassuring police and prosecutors that while they don’t have much to tell them now, they hope to provide more information and possibly help in the near future.

For months, the FBI had been unable to open the phone—a 5C model—and was engaged in a high-stakes legal battle with Apple Inc. trying to force the company to help open the device. The Justice Department ended the legal battle this week, when it said a third party outside the U.S. government had shown the Justice Department a new means of cracking the phone.

"That method for unlocking that specific iPhone proved successful," the FBI missive said, adding that the agency is aware that the difficulty of accessing locked data in criminal probes “is a substantial state and local law-enforcement challenge that you face daily.’’

The FBI is now testing to see whether the method used in the San Bernardino case may work against other types of iPhones, people familiar with the matter said.

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