Among actions that could draw retaliation under the order would be attacks that target vital resources like power grids; steal money, trade secrets or personal information; or disrupt large computer networks. The government could penalize those responsible by freezing assets in the United States, barring Americans from doing business with them and blocking them from entering the country. They would be cut off from American goods and technology.

The sanctions in the Sony case were based on existing authority specifically targeting North Korea, but the new order has no geographic limits, mirroring the approach to counterterrorism, counternarcotics and transnational criminal organizations. “This allows us to target the activity itself wherever it arises,” said John E. Smith, acting director of the Treasury Department’s Office of Foreign Assets Control, which enforces sanctions.

The administration named no initial targets, although it has plenty of cases. American authorities have identified Russian and Chinese hackers tied to past attacks. But the imposition of sanctions, like last year’s indictment of five Chinese members of the People’s Liberation Army charged in the theft of data from American companies, is a delicate diplomatic move that risks shutting off help from a foreign government in tracking down targets on its soil.

Identifying perpetrators may be a particular challenge. In contrast to states like North Korea or Russia that are sanctioned for traditional violations of international norms, hackers dwell in a murky digital world cloaked in ways that make them difficult to catch. In attacks on JPMorgan Chase, Target and Home Depot, for instance, it has been hard to identify the culprits.

The administration tried to reassure the technology world that the new powers would be used judiciously. “We will not, certainly, be using this to target free speech or interfering with the free and open Internet, and we’re not going to be going after the innocent victims of people whose computers were taken over and used by malicious actors,” said Michael Daniel, the president’s online security coordinator.