News organizations contend that the calls, which local officials say can be ghastly in their representations of suffering and violence, will allow for a public review of the police response to the attack.

“We think it will help in fully evaluating law enforcement’s response, and it could be law enforcement responded appropriately,” said Rachel E. Fugate, a lawyer for the news media outlets that sued Orlando.

But some members of victims’ families insisted that releasing the calls would only aggravate the trauma associated with the killings.

“The problem is the unknown version of what’s contained on the recordings and not knowing if the tragic cry for help would be the voice of a personal loved one and knowing there was nothing that could’ve been done to help them,” Rosetta Evans, the mother of a man who died in the attack, told Judge Schreiber in a letter.

Urging “total respect” for the victims and their relatives, Ms. Evans said she would be “very, very disappointed for the media to gain access to such sensitive material only to exploit it.”

A lawyer for the city, Darryl M. Bloodworth, made a similar argument after Monday’s hearing.

“The truth is some people do not have the same sensitivity that others do, and if the media gets ahold of them, they can be used to continue the pain and misery for the families who have suffered enough,” he said.