Garner, a 43-year-old father of six, could be heard on an amateur video shouting "I can't breathe!" as Officer Daniel Pantaleo placed him in an apparent chokehold. Police said the officers were arresting Garner on suspicion of selling loose, untaxed cigarettes.
A second video, which appeared to have been shot shortly after Garner was handcuffed, showed him lying on the sidewalk, apparently unresponsive. More than three minutes in, medics arrive and one checks his pulse. Garner is lifted onto a gurney and transported to a waiting ambulance about two minutes later.
A bystander asks why no one is performing CPR and one officer responds, "because he's breathing."
Garner, who had asthma, died a short time later.
Donovan said his decision to take the case to a grand jury was based on his office's investigation and the medical examiner's ruling that the death was a homicide caused by neck compressions from the chokehold, chest compression and Garner's prone position while being restrained.
Donovan said a court granted his request for the extra grand jury on Monday. He said in a statement that he would make no additional comment about the panel's work, including possible witnesses and charges, to maintain proceedings' secrecy.
Pantaleo, an eight-year NYPD veteran, was stripped of his gun and badge after Garner's death and another officer was placed on desk duty. Two paramedics and two emergency medical technicians were suspended without pay.
Pantaleo's lawyer, Stuart London, said it was too early to say whether his client would testify before the grand jury.
"That's a decision that I weigh very carefully," London said.
Patrick Lynch, the president of the Patrolmen's Benevolent Association, said the union expected a grand jury investigation and is encouraged that the process is moving forward.
"We are confident that a fair and impartial grand jury that is allowed to conduct its deliberations based on facts and not emotion or political considerations will see that justice is served," Lynch said in a statement.
Civil rights leader the Rev. Al Sharpton plans to lead a march to Donovan's office on Saturday. Protesters are calling for Donovan to file criminal charges or let federal prosecutors take over.
Several members of New York's congressional delegation last week echoed the call for the Justice Department to investigate.
They questioned whether Donovan, a Republican, could adequately investigate the case given his close working relationship with police and the borough's large population of police officers.
Sharpton said he, Garner's family and the family's lawyers will meet Thursday with U.S. Attorney Loretta Lynch to reiterate their desire for a federal investigation.