Scores of people were already lying dead or injured inside a crowded Orlando nightclub, and the police had spent hours trying to connect with the gunman and end the situation without further violence. But when Omar Mateen threatened to set off explosives, the police decided to act, and pushed their way through a wall to end the bloody standoff.

That was a critical decision — one of many made by the police early on Sunday during the mass shooting at Pulse, a gay nightclub, that left 50 people dead, including the gunman, the authorities said.

A day after the shooting, many details of the police response remained in question, and the police account continued to contain crucial gaps — perhaps most critically, what happened during the hours that Mr. Mateen was hiding in a nightclub bathroom as he spoke intermittently to the police by cellphone.

But law enforcement experts said that based on the initial accounts, the Orlando police appeared to have acted appropriately, following well-established tactical protocols that may have prevented further carnage, despite a nearly three-hour gap between when the shooting started and when Mr. Mateen, 29, was killed by police officers.

The officers “acted very heroically and courageous and saved many, many lives during this operation,” said John Mina, Orlando’s police chief, at a news conference on Monday. Jeffrey L. Ashton, the Orange County state attorney, announced on Monday that his office would work with the Florida Department of Law Enforcement to investigate the use of force by the police once the criminal investigation, led by the F.B.I., was concluded.

The authorities on Monday described a complicated series of events and a changing crime scene that forced them to shift their tactics. Protocols have changed since the Columbine High School massacre in 1999, but the evolving situation in the club led the police to use both the current tactics of moving forcefully against a gunman, and the former strategy of stalling and buying time to draw the gunman out.

According to the authorities, the first police officers arrived on the scene not long after Mr. Mateen opened fire with an assault rifle and pistol. Shots were exchanged in two separate bursts, but then Mr. Mateen retreated to the bathroom, where he connected with the police by phone. The police waited for nearly three hours, they said, to try to convince Mr. Mateen to surrender.

That approach continued until Mr. Mateen threatened to deploy explosives, including what the authorities described as a bomb vest, which prompted officers to discard the notion that they were facing a barricaded hostage situation. No explosives were found.

“If there is a window of opportunity for us to resolve the situation peacefully, we’ll take advantage of it,” said Ed Allen, training program manager at the National Tactical Officers Association. “But when the suspect escalates the level of violence, we are forced to intervene.”