One council member said they are not ignoring issues - they are just being cautious.
"Right now, staff has the mandate in front of them, and they are letting us know what it's going to take to make it happen and make it happened in an orderly fashion," said Councilman Robert Massey.
The Fayetteville Police Department drew criticism late last year when it was revealed statistics show 75 percent of all drivers stopped and searched are African-American. Bergamine has denied his officers are involved in racial profiling - instead saying most of the stops were in high population and high crime areas.
In meetings and at public forums last year, Bergamine defended consent searches, calling it a good tool to seize illegal weapons and drugs.
In October, the council approved a new traffic policy with a five-point plan that documents search reasons, tracks location and time of stops and searches, puts video cameras in police cars and establishes public meetings for citizens to provide input. But critics say the new policy doesn't go far enough.
At Monday night's city council meeting, most members said informally they support a four-month moratorium on police consent searches while an outside agency reviews the department policy.
Local NAACP leaders said it was a good first step towards restoring public trust.
"We are not saying to stop searching people, if there is probable cause. By all means stop them, but when you stop a person just because of what they look like, or you have a hunch, there is something wrong with that," said Jimmy Buxton of the local NAACP.
Buxton also said the community has to be part of the process of selecting a new chief to replace Bergamine who retires June 30.