President Biden warned President Vladimir V. Putin of Russia on Friday that time was running out for him to rein in the ransomware groups striking the United States, telegraphing that this could be Mr. Putin’s final chance to take action on Russia’s harboring of cybercriminals before the United States moved to dismantle the threat.

In Mr. Biden’s starkest warning yet, he conveyed in a phone call to Mr. Putin that the attacks would no longer be treated only as criminal acts, but as national security threats — and thus may provoke a far more severe response, administration officials said. It is a rationale that has echoes of the legal justification used by the United States and other nations when they cross inside another country’s borders to rout terrorist groups or drug cartels.

“I made it very clear to him that the United States expects, when a ransomware operation is coming from his soil, even though it’s not sponsored by the state, we expect them to act if we give them enough information to act on who that is,” Mr. Biden told reporters.

Later, as he was leaving for Delaware for the weekend, Mr. Biden appeared to specify one of the ways the United States could respond. Asked if it might attack the servers Russian cybercriminals have used to hijack American networks — meaning knock them offline — Mr. Biden responded, “Yes,” according to a pool report.