Obama said at his prime-time press conference Wednesday that white officer Crowley had "acted stupidly" in the arrest of African-American Harvard professor Henry Louis Gates, a racially-infused case that has sparked a national debate on race.
On Friday, a multiracial group of police officers asked the President to apologize for comments union leaders called insulting.
Officers said they resent any implication that race played a role in Crowley's arrest of Gates at his home near Harvard University.
Union leaders said Crowley acted appropriately when he arrested the scholar on charges of disorderly conduct.
Police said Gates flew into a rage when officers responding to a report of a burglary asked him to show identification.
Obama has not apologized for the comment but said he had called Crowley to explain that he never meant to insult the officer.