“They think that the escalation ceiling, beyond which Pakistan will be forced to respond, is higher than previously assessed, and therefore they are willing to do more than India has done previously,” said Ashok Malik, a senior fellow at the Observer Research Foundation, a policy organization based in New Delhi.

“India was exercising cross-L.O.C. options that were very close to doing nothing,” he said, referring to the Line of Control. “It is willing to go a little further.”

Delhi may also be counting on intervention from Washington, which is cultivating a closer strategic relationship with India, and which could put pressure on Pakistan not to retaliate, said Myra MacDonald, the author of “Defeat is an Orphan: How Pakistan Lost the Great South Asian War.”

“If it does turn out to be a one-off, yes, they could have set a new norm in terms of how they respond to attacks,” she said. The shift, she said, reflected India’s growing confidence in its “diplomatic cover.”

“Nobody is really going rally to support Pakistan on this,” she said.

Hours before the strike was reportedly begun, the United States national security adviser, Susan E. Rice, spoke by telephone with her Indian counterpart, Ajit Doval. Ms. Rice’s office released a statement critical of Pakistan, saying the United States expects Islamabad to “take effective action” to combat terrorist groups.

The news sent tremors through Indian financial markets, with the country’s benchmark stock index, the Sensex, plunging 465 points, or around 1.6 percent. But social media erupted with congratulations for Mr. Modi.

Local residents reported heavy shelling near the Pakistani border, and villagers took shelter in underground bunkers used during previous violations of the cease-fire along the Line of Control.