The President's statement comes as American cities brace themselves for race riots following the acquittal of the vigilante who shot the unarmed black teenager.
George Zimmerman shot Trayvon Martin as the 17-year-old was returning from a trip to the shops.
Prosecutors said Zimmerman was a ‘wannabe cop’ who identified his victim as a potential troublemaker simply by ‘racial profiling’.
But jurors accepted the 29-year-old’s claim that he had acted in self-defence after the teenager attacked him.
He said: 'I know this case has elicited strong passions. And in the wake of the verdict, I know those passions may be running even higher.
‘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.'
Protest marches were held within hours of Saturday night’s verdict and violence was reported as far away as Oakland in California.
Gangs of youths attacked police and attempted to set cars on fire while others smashed windows in a downtown area.
Police swamped the town of Sanford, Florida, where the trial took place and the gated estate where Trayvon was killed was barricaded off to stop any demonstrations.
Officers have put in place plans to stop youths from forming ‘flash mobs’ having learned from the London riots where gangs used social media to organise.
Zimmerman went into hiding immediately after the verdict. He was described as a ‘dead man walking’, having received numerous death threats.
The neighbourhood watch volunteer killed Trayvon in February last year after he spotted the hooded Miami teenager who was visiting a family friend.
Zimmerman called police to report an intruder and followed Trayvon in his car. At some point the pair got into a fight and Trayvon was shot once in the chest.
Police in Sanford, which is about 30 miles from Orlando, initially failed to arrest Zimmerman.