It comes in response to recent officer-involved shootings and allegations of discrimination within the city's police force.
There were some strong words at the crowded council meeting.
"The City of Medicine is sick," said defense attorney David Hall. "It has a runny nose and I'm sick of being the Kleenex on the runny nose of Durham."
Hall urged city leaders to participate in racial equity training after recent events involving the police department including a fatal officer involved shooting, allegations of discrimination among its ranks, and an alleged comment made by the police chief after Hall was shot in a drive-by shooting.
"That is the ugliness of institutional racism," said Hall. "Racism is an institution and it doesn't care who is at the helm."
"We believe the traffic stops and searches in Durham are directly related to the war on drugs in Durham and that these stops disproportionately affect Durham's black and Latino community," said Megan McDowell with Fostering Alternative Drug Enforcement.
Hall's supporters say community tensions are running high, and that was apparent at Thursday's meeting. Several people who signed up to speak felt silenced.
"How many of our citizens are able to come out at 1 o'clock during the day to speak to issues that matter," said Tia Hall. "It's disappointing."
Mayor Bill Bell responded to the standing room only crowd.
"I don't take any of this as a joke," said Bell. "I take it very seriously."
Bell made a promise. He vowed to start a dialogue about race through the city's longstanding Human Relations Commission.
"I can tell you that I will be involved in it," said Bell. "I will take an active role in listening and being a part of this discussion."
The mayor went on to say that those public discussions will happen soon and it won't be a drawn out process.
Hall says if the Human Relations Commission is the only way to get city leaders to come to the table, he'll take it.