President Barack Obama urged Americans to do some 'soul searching' on Friday after the killing of an unarmed black teenager by a neighborhood watch guard that has sparked outrage across the nation.

"If I had a son he would look like Trayvon," Obama, the country's first African American president, told reporters, as he called the fatal shooting of 17-year-old Trayvon Martin a 'tragedy'.

"I think all of us have to do soul searching to figure out how does something like this happen and that means we examine the laws and the context for what happened."

Up to 20,000 people demanding justice rallied late Thursday in the Florida town of Sanford where Martin was shot dead by volunteer neighborhood watch guard George Zimmerman in late February in a gated community.

The mostly African-American crowd demanded the arrest of Zimmerman, who claims he acted in self-defense after a confrontation with the teenager. Zimmerman has been neither detained nor charged with any crime.

Protesters have claimed that Martin's killing is just the last example of racial profiling and unjust treatment of blacks by the country's criminal justice system.

An online petition has gathered more than a million signatures following Martin's fatal shooting on February 26, and the Department of Justice has launched an investigation into the events.

The FBI, the state attorney's office and the Florida Department of Law Enforcement are also investigating the case.

Local police say they believe Zimmerman cannot be prosecuted thanks to a Florida law that lets state residents use lethal force in self-defense.

"Obviously, this is a tragedy. I can only imagine these parents are going through. And when I think about this boy I think about my own kids," Obama said, addressing reporters in the White House Rose Garden.

He said Martin's parents "are right to expect that all of us as Americans are going to take this with the seriousness it deserves and we'll get to the bottom of what happened.

"And I think every parent in America should be able to understand why it's imperative we investigate every aspect of this and everybody pulls together, federal, state and local, to figure out exactly how this tragedy happened."

Sanford police chief Bill Lee, who has been criticized for failing to arrest Zimmerman, announced just ahead of Thursday night's rally that he was temporarily leaving his post because he had become a "distraction."

But the victim's father, Tracy Martin, has demanded further action.

"The temporary stepdown of Lee is nothing. We want an arrest. We want a conviction and we want an arrest of the murderer of our son," he told the crowd late Thursday.

Those crying for Zimmerman's arrest have noted that he called the police several times while tracking the actions of the teenager, whom he said looked "real suspicious," according to transcripts released by police.

Martin's parents said he had just gone to the store to buy some candy.

Although dispatchers told him not to pursue the youngster, Zimmerman apparently followed him anyway and shot him with his 9mm handgun. The exact circumstances of the shooting, however, remain unclear.