"Last week was an emotional and hard week as we saw extreme acts of violence against black men across our country as well as against police officers in Dallas", he wrote.
Yanez's attorney has said the officer reacted after seeing a gun, and that one of the reasons he pulled Castile over was because he thought he looked like a "possible match" for an armed robbery suspect.
The audio recording, which was given by a viewer to Minneapolis' KARE-TV Tuesday, is purportedly police radio traffic from the time Castile's vehicle was pulled over Thursday.
City Hall and the St. Anthony Police Department were closed for the day and no officials from the city were visible.
Castile's death was one of two deaths of African American men by police officers in the U.S. last week, which brought the attention of the nation to the question of what appears to be an overabundance of the death black men at the hands of law enforcement.
TV Judge Glenda Hatchett, left, addresses the media as Valerie Castile, the mother of Philando Castile, listens during a news conference on the State Capitol grounds Tuesday, July 12, 2016, in St. Paul, Minn. St. Anthony, as well as Lauderdale and Falcon Heights, according to a news release from Falcon Heights, will be temporarily patrolled by squad cars from other area police agencies in the coming days. A message seeking comment from the community's mayor, Jerry Faust, was not immediately returned.
Valerie Castile stressed that her son got his permit because he had a right to carry a weapon - not because he felt his life was in danger.
A 2001 study of 65 other Minnesota jurisdictions found officers stopped and searched minority drivers at greater rates than whites.
The data provided by the department does not give details about individual arrests, nor does it show when an arrestee was also issued a citation. The department's annual reports show the vast majority of its arrests stem from traffic-related offenses.
St. Anthony is a suburb north of St. Paul.