The slain teen's parents used social media to thank supporters following Saturday's not guilty verdict in the Florida murder trial of Zimmerman.
Martin's family did not address the acquittal of their son's killer in a brief series of Twitter messages; however, supporters in California and Washington took to the streets overnight to express their disagreement with the verdict.
In a statement issued by the White House, Obama urged Americans to respect the justice system.
"The death of Trayvon Martin was a tragedy. Not just for his family, or for any one community, but for America. I know this case has elicited strong passions. And in the wake of the verdict, I know those passions may be running even higher," he said. "But we are a nation of laws, and a jury has spoken.
"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. 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. We should ask ourselves, as individuals and as a society, how we can prevent future tragedies like this. As citizens, that's a job for all of us. That's the way to honor Trayvon Martin."
Martin's family was not present the acquittal verdict was handed down by the six-woman jury deciding the fate of Zimmerman, who was charged with second-degree murder for killing the unarmed 17-year-old in a gated community in Sanford, Fla., on Feb. 26, 2012, the Orlando Sentinel reported.
Moments after the verdict was read, the youth's father, Tracy Martin, tweeted: "God blessed Me & Sybrina with Tray and even in his death I know my baby proud of the FIGHT we along with all of you put up for him GOD BLESS."
In a second tweet, Martin said: "Thanks to everyone who are with us and who will be with us (so) we together can make sure that this doesn't happen again."
Sybrina Fulton, Trayvon's mother, thanked supporters later: "Lord during my darkest hour I lean on you. You are all that I have. At the end of the day, GOD is still in control. Thank you all for your prayers and support. I will love you forever Trayvon!!! In the name of Jesus!!!"
"Et tu, America?" Trayvon's brother, Jahvaris Fulton, tweeted.
In San Francisco and Oakland, Calif., residents took to the streets to vent their frustrations with the verdict.
Several hundred people attended a rally and peacefully marched through San Francisco. A smaller but rowdier march across the bay in Oakland left a trail of broken windows, small fires and graffiti in its wake, the Oakland Tribune reported. There were no injuries or arrests.
The verdict was the subject of a protest march in Washington early Sunday. Demonstrators took to the streets of the capital's Adams Morgan and Columbia Heights neighborhoods with signs and chants supporting Martin and criticizing laws supposedly slanted toward protecting whites.
The Washington Post said the size of the crowd ebbed and flowed, but at one point appeared include several hundred young people, including several whites.
The protest began about midnight in areas known for an active nightlife, but caused minimal disruptions to traffic, the Post said.
Meanwhile, NAACP officials called for civil charges to be brought against Zimmerman, the Detroit Free Press reported.
"We pray that the Justice Department will act," said the Rev. Wendell Anthony, president of the Detroit Branch of the NAACP. "We don't want anything special, we just want justice."