Last month, Mr. Biden used the summit with Mr. Putin to make the case that ransomware was emerging as an even larger threat, causing the kind of economic disruption that no state could tolerate. Mr. Biden specifically cited the halting of the flow of gasoline on the East Coast after an attack on Colonial Pipeline in June, as well as the shutdown of major meat-processing plants and earlier ransomware attacks that paralyzed hospitals.

The issue has become so urgent that it has begun shifting the negotiations between Washington and Moscow, raising the control of digital weapons to a level of urgency previously seen largely in nuclear arms control negotiations. On Tuesday, the White House press secretary, Jen Psaki, said American officials will meet with Russian officials next week to discuss ransomware attacks — a dialogue the two leaders had agreed upon at their summit in Geneva.

On Saturday, as the attacks were underway, Mr. Putin gave a speech timed to the rollout of Russia’s latest national security strategy that outlines measures to respond to foreign influence. The document claimed that Russian “traditional spiritual-moral and cultural-historical values are under active attack from the U.S. and its allies.”

While the strategy reaffirmed Moscow’s commitment to using diplomacy to resolve conflicts, it stressed that Russia “considers it legitimate to take symmetrical and asymmetric measures” to prevent “unfriendly actions” by foreign states.

The remarks, cybersecurity experts said, were Mr. Putin’s response to the summit with Mr. Biden.

“Biden did a good job laying down a marker, but when you’re a thug, the first thing you do is test that red line,” said James A. Lewis, a cybersecurity expert at the Center for Strategic and International Studies in Washington. “And that’s what we’re seeing here.”

Mr. Lewis added that “low-end penalties” like sanctions had been exhausted. “The White House will have to use more aggressive measures, whether that is something in cyberspace, or a more painful legal or financial maneuver,” he said.

Stronger measures have long been debated, and occasionally used. When Russian…