Obama called for peace Sunday and acknowledged the Zimmerman case has stirred strong emotions.
"I now ask every American to respect the call for calm reflection from two parents who lost their young son. And as we do, we should ask ourselves if we're doing all we can to widen the circle of compassion and understanding in our own communities," he said.
"We should ask ourselves if we're doing all we can to stem the tide of gun violence that claims too many lives across this country on a daily basis," Obama said.
One critic of the verdict, Terri Weems, said the trial was a referendum on race that confirmed what she said Martin supporters knew all along.
"That's our society," she said as she headed into church in Washington on Sunday. "We expected not to be given justice. We haven't been dealt justice all this time. ... It's very disheartening."
NAACP President Benjamin Jealous said on CNN's "State of the Union" on Sunday that the largely peaceful nature of the protests is a positive sign.
"I think we should, frankly, right now be celebrating the fact that we've seen a generation of young people respond by using our system, raising their voices, but not using their fists," he said.