But Holder, speaking to an African American sorority, was silent on whether the Justice Department would pursue civil rights charges against George Zimmerman, the neighbourhood watch volunteer acquitted late Saturday of Martin's killing.
"The Justice Department shares your concern -- I share your concern -- and, as we first acknowledged last spring, we have opened an investigation into the matter," Holder said.
"Independent of the legal determination that will be made, I believe that this tragedy provides yet another opportunity for our nation to speak honestly about the complicated and emotionally-charged issues that this case has raised," he said.
"He has no opinion to express about the disposition of how the Justice Department would look at this," said Carney.
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Obama appealed for calm yesterday after the verdict was handed down in Florida, setting off a wave of angry protests in US cities.
"We should ask ourselves, as individuals and as a society, how we can prevent future tragedies like this," Obama said.
"As citizens, that's a job for all of us. That's the way to honour Trayvon Martin."
The defence successfully argued that Zimmerman -- who is half white and half Latino -- fired his handgun in self-defence after the teen wrestled him to the ground and started slamming his head against the pavement.
Critics of the verdict argue that Zimmerman racially profiled the unarmed black teen -- who had no criminal record -- and was able to kill him with impunity because of a biased criminal justice system.