President Obama vowed Wednesday that he would not "let up" in his push to address law enforcement issues after a grand jury in New York opted not to bring criminal charges in the case of Eric Garner, a black man killed when a white police officer placed him in a chokehold.

"It is incumbent upon all of us as Americans, regardless of race, region, faith, that we recognize this is an American problem and not just a black problem or a brown problem or a Native American problem; this is an American problem.

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"When anybody in this country is not being treated equally under the law, that’s a problem. And it’s my job as president to help solve it," he said.

Obama said the Garner case speaks "to the larger issues we've been talking about now for the last week, the last month, the last year and sadly for decades."

"Unfortunately, we are seeing too many incidences where people just do not have confidence that folks are being treated fairly," Obama said.

The president said he had spoken to Attorney General Eric Holder on the phone, and that the Justice Department would have additional information about the federal response to the grand jury finding.

But Obama said the White House was committed to taking "specific steps to improve the training" of police officers and that the Justice Department would "be scrupulous in investigating cases where we're concerned about the impartiality and accountability that's taking place."

The president said he was "committed that we have a country where everybody believes in the core principle that we are equal under the law."

The decision in the Garner case comes on the heels of a similar decision in the shooting death of Michael Brown, a black teenager who was killed by Ferguson, Mo., police officer Darren Wilson. A grand jury opted not to bring charges against Wilson, sparking a series of protests across the country, with demonstrators saying the case was emblematic of bias in the criminal justice system.

Earlier this week, Obama met with police, civil rights leaders, and elected officials from Ferguson and announced a series of administration steps to address concerns raised by the Brown case.

The president requested federal funding that could purchase 50,000 body-worn cameras for police officers, something the family of slain 18-year-old Michael Brown has lobbied for.

The White House is also moving to reform the way local police can get heavy military-style weapons and equipment, implementing new policies and training requirements from law enforcement that acquires supplies from the Pentagon.

And Obama is creating a new task force that will examine “how to promote effective crime reduction while building public trust,” a White House official said. The panel will be led by Philadelphia Police Commissioner Charles Ramsey and former Assistant Attorney General Laurie Robinson.