WASHINGTON (CNN) -- A new national poll indicates that white and black Americans don't see eye to eye on last month's arrest of Harvard University professor Henry Louis Gates.

The CNN/Opinion Research Corp. survey released Tuesday also suggests a racial divide over President Obama's initial comments on the incident.

The arrest sparked a national discussion on the issue of racial profiling, which was amplified when President Obama weighed in on the matter.

In a prime time news conference on July 22, Obama said "the Cambridge police acted stupidly in arresting somebody when there was already proof that they were in their own home."

Fifty-four percent of people questioned in the poll said they don't think Cambridge, Massachusetts, police office James Crowley acted "stupidly" when he arrested Gates at the professor's home after Crowley responded to a call that someone was breaking into the house.

Thirty-three percent said Crowley did act stupidly. But there's a major racial divide, with 59 percent of black respondents saying Crowley acted stupidly compared to 29 percent of whites questioned.

Fifty-three percent of those polled felt Gates acted stupidly in the incident, with 30 percent saying no. Broken down by race, 58 percent of whites said Gates acted stupidly, with African-Americans split on the question: 44 percent said yes and 43 percent said no.

Two days after Obama's remarks, after criticism from police unions and after speaking with Crowley, Obama said "because this has been ratcheting up, and I obviously helped to contribute ratcheting it up, I want to make clear that in my choice of words, I think, I unfortunately gave an impression that I was maligning the Cambridge Police Department or Sgt. [James] Crowley specifically and I could have calibrated those words differently. And I told this to Sgt. Crowley."

Fifty-four percent of people questioned said they think the president acted stupidly when he commented on the Gates arrest, with 32 percent disagreeing. But again, the poll indicates a racial divide, with 63 percent of whites feeling Obama acted stupidly and 26 percent of black respondents agreeing.

Sixty-one percent approve of how the president has handled race relations, with 92 percent of African-Americans and 56 percent of whites approving.

Did Obama's initial comments damage his political standing?

"One-third of whites say that Obama's comments about this matter made them feel less favorable toward him, compared to only 4 percent of whites who feel more favorably toward Obama due to his comments," said CNN Polling Director Keating Holland.

Sixty-six percent of whites said a white homeowner would have been arrested for the same behavior. Twenty-five percent of blacks agree.

The poll indicated that both blacks and whites believe Friday's "beer summit" at the White House, in which Obama was host at a meeting with Gates and Crowley, was a good idea. But was it a "teachable moment," as mentioned by the president?

"Not according to the public -- blacks and whites agree that the whole controversy did not teach Americans a lesson that will lead to better race relations," Holland said.