New York City is on track to close the year with the fewest murders since Elvis Presley appeared on “The Ed Sullivan Show.”

The New York Police Department has recorded 284 murders so far in 2017, putting the city on pace to finish the year with fewer than 300 murders for the first time since the 1950s. Murders in 2017 are down from 329 at the same point last year and 2,245 in 1990—the highest recorded number of murders by the NYPD.

Officials...