“This newly available option is one that is on the table,” said Josh Earnest, the White House press secretary.

Mr. Obama signed the executive order after the attack on Sony Pictures’ computer network, an intrusion that American officials believe was carried out by the government of North Korea. The order gives the administration the ability to freeze assets in the United States, bar Americans from doing business with groups that sponsor cyberattacks, and cut the groups off from American goods and technology. But the use of the sanctions authority could be more significant if Mr. Obama wielded it against China, which officials believe has continued to sponsor cyberattacks even as the two nations warily seek a working relationship in other areas.

Mr. Earnest declined to say whether investigators had concluded that the attacks at the personnel office affected many millions more people than the four million already announced. And he declined to say whether officials at the United States Embassy in China were being relocated out of a fear that the hackers retrieved information about their contacts in that country.

“We have acknowledged that potentially sensitive data about a substantial number of federal employees was breached or is at least now at risk,” Mr. Earnest said. “But we haven’t talked publicly about the details of that.”

Security experts say the forensic evidence from the attacks suggests that they were the work of a sophisticated Chinese group that for the past three years has targeted a number of government agencies and defense contractors.

More recently, however, the group appears to have been looking for inroads into the personal lives of government workers, military and intelligence personnel, and defense contractors, and it has been gathering the personal data and medical histories of its targets. Though experts say it is not clear what the attackers plan to use the information for, they note that it is the sort of delicate medical data that could be used for blackmail.

While the group is not a unit of the People’s Liberation Army’s Third Department, which oversees the Chinese military’s cyberintelligence gathering, the chronology of its attacks matches Beijing’s stated economic and strategic objectives.