Looking for lessons to draw from the shooting death of Trayvon Martin, President Barack Obama said Friday afternoon that the nation needs to do some "soul searching."

Delving directly and personally into the national debate over race and ethnicity in the aftermath of George Zimmerman's acquittal of killing Martin, Obama said the country needs to look for ways to bolster African-American boys and examine state and local laws to see if they encourage confrontations like the one in Florida.

"Where do we take this?" Obama wondered aloud in an impromptu appearance in the White House briefing room. "How do we learn some lessons from this and move in a positive direction?"

The president said it's time "for all of us to some soul searching," but he also said it's generally not productive when politicians try to orchestrate a conversation.

On the positive side, he said race relations in the United States actually are getting better.

Looking at his own daughters and their interactions with friends, the president said, "They're better than we are. They're better than we were."

The president declined to wade into the details of legal questions about the Florida case, saying, "Once the jury's spoken, that's how our system works."

But he said state and local laws, such as Florida's "stand your ground" statute, need a closer look.

Obama questioned whether a law that sends the message that someone who is armed "has the right to use those firearms even if there is a way for them to exit from a situation" really promotes the peace and security that people want.

And he raised the question of whether Martin himself, had he been armed, "could have stood his ground on that sidewalk" and shot neighborhood watch volunteer George Zimmerman if he felt threatened when being followed.

Though last year the president said Martin could have been his son, on Friday Obama likened the late teenager directly to himself, saying he could have been Martin 35 years ago.

Obama's appearance marked his first extended comments on the Martin case since Zimmerman was acquitted last weekend of second-degree murder and manslaughter charges in Martin's death last year. Jurors found that Zimmerman was acting in self-defense when he shot the unarmed 17-year-old.

Zimmerman identifies himself as Hispanic.

U.S. Attorney General Eric Holder has said the Justice Department has an open investigation into the case. The department is looking into whether Zimmerman violated Martin's civil rights.

George Zimmerman's brother, Robert Zimmerman, Jr., said he was glad to see the president speak about the societal impact his brother's case has had on the nation.

"People wanted to hear from the president and they heard from him," he said in a telephone interview immediately following the president's remarks.

I agree with the president that African-American youth, and of all colors need our encouragement. My brother is Hispanic, and he spent his time mentoring African-American youth to encourage them,” he said.

But he wouldn't have minded seeing the president touching on some points he omitted.

“Would I have liked the president to call for calm? Yes, there is plenty of evidence that things have gotten violent. Do I expect him to bring it up? It’s politics. I don’t have expectations that he’s going to say 'Please stop threatening the Zimmerman family.' And he didn’t."

Fox News Latino political analyst Juan Williams said the president's move was bold — and risky.

“This is a president who took a tremendous risk on what is the most polarizing issue in American history – which is race,” Williams said.

“We are a more diverse society, there are more black and Hispanic people, and some believe we don’t have to pay attention to race, but that’s a dodge,” Williams added. "Truth is we are an extremely race-conscious society. Any Hispanic mother or any black mother knows that.”

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