Officials on Monday released recordings of phone calls between authorities and the gunman in the June 12 nightclub massacre in Orlando, Fla., that left 49 people dead and more than 50 others injured.

While officials had provided written transcripts of the calls in September, the audio recordings provide the first opportunity to hear the gunman, Omar Mateen, as he spoke to an Orlando police negotiator while holed up in the Pulse nightclub with hostages.

In...