Obama's remarks came hours after a news conference held by Cambridge police union officials, who said the president must apologize. Crowley was there but didn't speak.
Without a full picture of what happened, Obama should have stayed out of the discussion, union officials said. Particularly hurtful was Obama's attempt to link the arrest to racial profiling by law enforcement, they said.
Sgt. Dennis O'Connor, president of the Cambridge Police Superior Officers Association, said: "Whatever may be the history, the supervisors and the patrol officers of the Cambridge Police Department deeply resent the implication and reject any suggestion that in this case or any other case they have allowed a person's race to direct their activities."
Stephen Killion, president of the Cambridge police union, said, "I think the president should make an apology to all law enforcement personnel throughout the entire country who took offense to this."
The matter escalated Monday, when word broke that Gates, 58, had been arrested five days earlier at the two-story home he rents from Harvard.
Supporters including Al Sharpton and the Rev. Jesse L. Jackson called the arrest an outrageous act of racial profiling. Public interest increased when a photograph surfaced of the handcuffed Gates being escorted off his porch amid three officers, two white and one black.
Cambridge police moved to drop the disorderly conduct charge Tuesday - without apology, but calling the case "regrettable."
That didn't end the debate: Some said Gates was responsible for his own arrest because of his response to Crowley, while others said Gates was justified.
Obama's criticism added fuel to the racial debate.
The backlash from police follows months of relatively smooth relations between the White House and law enforcement. The biggest police union, the Fraternal Order of Police, did not endorse Obama in the 2008 election. Still, its leaders spoke in favor of Obama's nominations of Eric H. Holder to be attorney general and of Judge Sonia Sotomayor to the Supreme Court.
Also, police groups were pleased that Obama had directed billions of dollars in stimulus funds to policing.
Jim Pasco, executive director of the Fraternal Order of Police, said he had been "taken aback" by Obama's criticism of the Cambridge police. "He had been pretty good to law enforcement," Pasco said.
