The justices seemed at odds over how to address the issue. Several said the problem was that the level of detail in Mr. Carpenter’s phone records violated his reasonable expectation of privacy. Others, notably Justice Neil M. Gorsuch, took a different approach, saying the problem was that the records were his property and should not have been disclosed without his consent or a warrant.

Michael R. Dreeben, a lawyer for the federal government, urged the justices not to take drastic action. “The technology here is new,” he said, “but the legal principles that this court has articulated under the Fourth Amendment are not.”

Recent Supreme Court decisions have expressed uneasiness with allowing the government to have unfettered access to vast amounts of digital data. The court limited the government’s ability to use GPS devices to track suspects’ movements in 2012 in United States v. Jones, and it required a warrant to search the cellphones of people placed under arrest in 2014 in Riley v. California.

Justice Elena Kagan said the case concerning GPS devices provided a close analogy to the new case, particularly as cell tower location data becomes more precise. “In both cases,” she said, “you have a new technology that allows for 24/7 tracking and a conclusion by a number of justices in Jones that that was an altogether new and different thing that did intrude on people’s expectations of who would be watching them when.”

But the majority in the Jones decision relied on property rights to justify the ruling, saying the police were not entitled to attach a device to a suspect’s car. Justice Gorsuch indicated that a similar theory could justify a ruling for Mr. Carpenter.

“One thing Jones taught us — and reminded us, really — is that the property-based approach to privacy also has to be considered, not just the reasonable expectation approach,” he said.

Older cases have concluded that information turned over to third parties is fair game. In 1979, in Smith v. Maryland, for instance, the Supreme Court ruled that a robbery suspect had no reasonable expectation that his right to privacy extended to the numbers dialed from his landline telephone. In 1976, in United States v. Miller, the court said much the same thing about bank records.