But U.S. Attorney General Eric Holder confirmed late Wednesday that the department is opening a probe into Garner's death.
"I will continue these conversations as we seek to restore trust, to rebuild understanding, and to foster cooperation between law enforcement and the communities they serve," during the probe, Holder said.
Holder emphasized the rift that has emerged between police and communities.
"We must seek to heal the breakdown in trust we have seen," he said.
As CBS2 Political Reporter Marcia Kramer reported, Officer Daniel Pantaleo, who put Garner in the apparent chokehold, also faces a full department probe from the NYPD. The administrative investigation will look at all the elements of the event, including the actions of all officers present.
Sources said the NYPD probe will specifically try to determine whether Pantaleo used a chokehold, which is not illegal in New York, but is against department policy.
Garner, a 43-year-old father of six, died in July after police officers attempted to arrest him for allegedly selling loose, untaxed cigarettes.
Jonathon Moore, an attorney for Garner's family, said he is "astonished by the (grand jury) decision."
Pantaleo released a statement, saying: "I became a police officer to help people and to protect those who can't protect themselves. It is never my intention to harm anyone and I feel very bad about the death of Mr. Garner. My family and I include him and his family in our prayers and I hope that they will accept my personal condolences for their loss."
Grand Jury Decides Not To Indict Cop In Eric Garner Chokehold Case
Esaw Garner, expressed no sympathy.
"Hell no," said Esaw Garner said. "The time for remorse would have been when my husband was screaming to breathe. That would have been the time for him to show some type of remorse or some type of care for another human being's life, when he was screaming 11 times that he can't breathe."
"No, I don't accept his apology," Esaw Garner continued. "No, I could care less about his condolences. No, I could care less. He's still working, he's still getting a paycheck, he's still feeding his kids, and my husband is six feet under, and I'm looking for a way to feed my kids now. Who's going to play Santa Claus for my grandkids this year? Cause he played Santa Claus for my grandkids -- who's going to do that now?"
The grand jury began hearing evidence in the case on Sept. 29, which included testimony by Pantaleo.
"He testified in the grand jury that he utilized the techniques that he was trained with in the police academy," Pantaleo's attorney, Stuart London, told CBS2's Kramer. "He was attempting to do a take-down move, which he was taught in the academy. He never intended to apply any force to the individual's neck, and any contact with the neck was incidental."
Staten Island District Attorney Daniel Donovan released a statement saying his office conducted a thorough investigation before presenting evidence to the grand jury. He added that he has applied for a court order to release specific information in the case to the public, which is required under state law.
"As this grand jury was dedicated to hearing only evidence regarding the circumstances surrounding Eric Garner's death, it was afforded the opportunity to singularly focus on the evidence in this case, and this case only, and to hear from all witnesses with any material evidence to offer, as well as expert witnesses, and to consider documentary and photographic evidence, in order to ensure that a thorough, just and fair investigation was accomplished," Donovan said.
Anticipating protests, de Blasio and Staten Island Borough President James Oddo appealed to people to keep the peace.
Addressing the media at Mount Sinai United Christian Church on Staten Island, the mayor said he spoke with Garner's father, Ben, who he said told him: "There can't be violence. Eric would not have wanted violence."
Said Oddo: "In this matter, the Garner family, the NYPD and the office of the Borough President speak with one voice when we say that disagreeing with the conclusion of the grand jury is your absolute right, and so is peacefully protesting the result and advocating for change."
De Blasio called it a "very emotional day" for the city.
"It's a very painful day for so many New Yorkers," the mayor said. "That is the core reality. So many people in this city are feeling pain right now, and we're grieving, again, over the loss of Eric Garner, who was a father, a husband, a son, a good man, a man who should be with us and isn't."
The case has also "put in stark perspective the relationship between police and community," de Blasio said. "These issues have come to the fore again, and we have to address them. We have to address them with all our might."
President Barack Obama said the Garner case "speaks to the larger issues that we've been talking about now for the last week, the last month, the last year and, sadly, for decades, and that is the concern on the part of too many minority communities that law enforcement is not working with them and dealing with them in a fair way."
Obama this week formed a task force aimed at strengthening the relationship between police and minority communities.
"I'm not interested in talk; I'm interested in action," the president added. "I am absolutely committed as president of the United States to making sure that we have a country in which everyone believes in the core principle that we are equal under the law."
De Blasio said he spoke Wednesday evening with Holder and U.S. Attorney Loretta Lynch, whom Obama has tapped to succeed Holder, and that they assured him the federal investigation in the case will move forward.
"It was a palpable sense of resolve," the mayor said. "The federal government will exercise its responsibilities here and do a full and thorough investigation."
Pantaleo also faces a civil lawsuit by the Garner family and possible departmental charges.
"The next action ... will be within the department for us to review if there are any violations of our administrative processes," Police Commissioner Bill Bratton said.
Sources told CBS2 one of the things the department will study is whether Pantaleo peformed a take-down maneuver or a chokehold, which is prohibited by the NYPD but is not illegal under state law.
London told 1010 WINS that Pantaleo would like to remain on the police force, but he's "taking it one day at a time." The officer is currently on modified duty performing crime analysis.
In cellphone video of the incident, Pantaleo, who is white, is seen placing his arm around Garner's neck and then taking him to the ground after Garner refuses to be handcuffed.
Garner, who was black, is heard saying repeatedly, "I can't breathe!" He died a short time later.
The New York City Medical Examiner's office ruled Garner's death a homicide, caused by the officer's apparent chokehold as well as chest and neck compressions and prone positioning "during physical restraint by police."
An independent forensic investigator hired by the Garner family also agreed with the medical examiner's findings.
Law experts said the grand jury was likely considering charges that included manslaughter, criminally negligent homicide and reckless endangerment against Panteleo.
Twelve of the 23 jurors needed to be in agreement for any charges to be filed, CBS2's Janelle Burrell reported.
Other officers seen on the video restraining Garner on the ground were given immunity in return for their testimony, WCBS 880's Irene Cornell reported. Bratton, however, said the NYPD will also investigate their actions.
Patrick Lynch, president of Patrolmen's Benevolent Association, released a statement, saying: "While we are pleased with the Grand Jury's decision, there are no winners here today. There was a loss of life that both a family and a police officer will always have to live with. It is clear that the officer's intention was to do nothing more than take Mr. Garner into custody as instructed and that he used the take down technique that he learned in the academy when Mr. Garner refused."
Bratton said Wednesday morning the NYPD was preparing for protests and that extra police officers would be on hand on Staten Island.
Speaking on "CBS This Morning," Bratton said he didn't anticipate any violence in New York City, but said "you hope for the best and plan for the worst."
Bratton said he's more concerned about outside agitators and spontaneous protests.
At police headquarters Wednesday night, loudspeakers were instructing all police personnel below the rank of captain to assemble in the auditorium with equipment to prepare for deployment, Kramer reported.
At Grand Central Terminal late Wednesday afternoon, a group of about 20 to 30 protesters was holding a "die-in," in which they laid on the floor, WCBS 880's Marla Diamond reported.
A coalition of organizations from the city announced earlier Wednesday they were planning to hold a protest after the grand jury decision was announced, regardless of the outcome, and they made good on those promises. Protesters flooded the West Side Highway, shutting down traffic near 51st Street.
Police penned the protesters with nets and gates at 48th Street.
A total of 17 people were arrested at different locations in Manhattan on citations for obstruction of vehicular traffic, police told CBS2.
Earlier, some protesters said they planned to disrupt the Christmas tree lighting ceremony at Rockefeller Center between 7 and 9 p.m., CBS2's Tony Aiello reported.
As CBS2's Tracee Carrasco reported, protesters had arrived at Rockefeller Plaza from Times Square by 6:15 p.m. Some were on the sidewalk chanting and holding signs, as others crowded the area for the annual holiday event.
But the NYPD would not let the protesters get anywhere near the Christmas tree.
Another demonstration will be held at Foley Square in lower Manhattan starting at 5:30 p.m. Thursday.
Using the rallying cry "this stops today" — words Garner said when police approached him on the day he died — protest groups have demanded that the NYPD take full accountability for instances of excessive and deadly force and end the department's "broken windows" policing strategy.
The NYPD vowed that it would take action if any Garner protests get out of hand.
Last week, thousands marched across Manhattan protesting the grand jury decision not to indict Officer Darren Wilson in the shooting that killed Michael Brown in Ferguson, Missouri -- a case that is also now the subject of a probe by the Department of Justice.
Protesters blocked an entrance to the Lincoln Tunnel and shut down the Queens-Midtown Tunnel, and also completely blocked traffic on the FDR Drive and the West Side Highway.
The controversy surrounding Garner's death prompted the NYPD to buy body cameras for its officers, who began training with the equipment this week.
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