In his remarks, Obama said demonstrations and other responses to the Zimmerman verdict must be non-violent or they will dishonor what happened to Martin and his family.
He outlined possible future steps, calling for the Justice Department, state governors and city mayors to work with law enforcement agencies "about training at the state and local levels in order to reduce the kind of mistrust in the system that sometimes currently exists."
For example, he noted that racial profiling legislation he pushed as a state senator in Illinois helped police departments think about the issue and act more professionally, which helped build trust with communities they serve.
Stand your ground laws
Obama also called for reconsideration of "stand your ground" self-defense laws in Florida and other states, that he said "may encourage the kinds of altercations and confrontations and tragedies that we saw in the Florida case, rather than diffuse potential altercations."
Sharpton and other civil rights leaders call for abolishing the "stand your ground" laws.
"If we're sending a message as a society in our communities that someone who is armed potentially has the right to use those firearms, even if there's a way for them to exit from a situation, is that really going to be contributing to the kind of peace and security and order that we'd like to see?" Obama asked.
To supporters of such laws, Obama said they should consider if the right to fight back with a gun would have applied to Martin.
"Do we actually think that he would have been justified in shooting Mr. Zimmerman, who had followed him in a car, because he felt threatened?" the president said. "And if the answer to that question is at least ambiguous, then it seems to me that we might want to examine those kinds of laws."
While rejecting any "grand new federal program," Obama also called for providing more support for African-American boys and young mans who disproportionately end up in prison or homicide victims.
No national conversation
However, he rejected calls for him to launch a national conversation on race, saying "I haven't seen that be particularly productive when, you know, politicians try to organize conversations."
His comment could have been a slap at his own response to the 2009 arrest of African-American university professor Henry Louis Gates by a white police officer responding to a report of a possible burglary at his Boston-area home.
After coming under criticism for saying police acted stupidly, Obama later invited the Harvard professor and the arresting officer for a beer at the White House.
On Friday, Obama instead endorsed "soul-searching" discussions in homes, churches and workplaces where people might be more honest about whether they were "wringing as much bias" out of themselves as possible.
"As difficult and challenging as this whole episode has been for a lot of people, I don't want us to lose sight that things are getting better," the president concluded, making a reference to his daughters' generation.
"It doesn't mean we're in a post-racial society. It doesn't mean that racism is eliminated," he said. "But, you know, when I talk to Malia and Sasha and I listen to their friends and I see them interact, they're better than we are. They're better than we were on these issues. And that's true in every community that I've visited all across the country."