Even before teams of armed terrorists struck Paris last month, briefly holding hostages in a theater, officials in New York had been altering their approach to school shootings and other murderous attacks that erupt and are frequently over within minutes.

Ordinary patrol officers, often armed with only a handgun and likely to arrive first at scenes like the one that unfolded on Friday at a Planned Parenthood clinic in Colorado, are now expected to head into an unfolding attack and confront the perpetrators without waiting for more heavily armed backup.

“If people are dying, you have to go in,” said John J. Miller, the deputy commissioner for counterterrorism and intelligence for the New York Police Department.

The approach is part of a shift in tactics in recent years as law enforcement agencies across the country rethink how to stop terrorist attacks already underway. Whereas a decade ago, officers might have tried to contain and negotiate with armed men holding civilians, now a consensus has taken hold among police officials, after attacks in Mumbai, India, and elsewhere, that the best way to save lives is to go in.