This undated family photo provided by the National Action Network...

This undated family photo provided by the National Action Network on Saturday, July 19, 2014 shows Eric Garner, who was confronted by police trying to arrest him on suspicion of selling untaxed, loose cigarettes on a Staten Island sidewalk, authorities said. Credit: AP

Allies of Bill de Blasio said Saturday that a man's death after an officer used a banned chokehold would show whether the mayor can deliver on campaign rhetoric to change the NYPD.

The police department is under fire after an amateur video showed officers attempting to arrest Eric Garner, 43, of Staten Island on Thursday on suspicion of selling untaxed cigarettes.

De Blasio, who rode to electoral victory on a wave of deep dissatisfaction in black and Latino communities about their treatment by police, called the video "very troubling." It shows an officer coming from behind to put Garner in a chokehold banned years ago by the NYPD, and Garner's head being slammed to the pavement. He is heard repeatedly whimpering, "I can't breathe."

Garner was adamant that he did not want to be arrested.

"Let me tell you. This is going to be a real test to see where policies are in the city now, and whether the change that we feel has occurred, has occurred," said the Rev. Al Sharpton, who led rallies Saturday at his Harlem headquarters and on Staten Island.

Said Public Advocate Letitia James: "This case will test our mettle as a city -- and as progressives."

De Blasio, who postponed his family vacation to Italy one day to deal with the uproar, spoke by telephone with Garner's widow, Esaw Garner, and mother, Gwen Carr, Saturday, said mayoral spokeswoman Marti Adams.

"He reassured the family that the city is doing everything possible to ensure a full and thorough investigation," Adams said.

"The issue is not whether one was selling cigarettes," Sharpton said. "The issue was how an unarmed man was subjected to a chokehold and the result is he is no longer with us."

As Sharpton spoke, Esaw Garner's knees buckled and he helped support her. She and Carr, also visibly distraught, had to be led away.

Garner's funeral is to be held at 7 p.m. Wednesday at Bethel Baptist Church, on Bergen Street in Brooklyn.

De Blasio and NYPD Commissioner William Bratton said that a final determination of any breaking of the law would come after an investigation by the Staten Island district attorney. But Saturday, Sharpton suggested that undue influence by the police union could undermine an inquiry. "I have very serious questions," he said.

Douglas Auer, a spokesman, sent a statement from District Attorney Daniel Donovan: "My office is working along with the NYPD to do a complete and thorough investigation into the circumstances surrounding Mr. Garner's death."

The NYPD Saturday identified Daniel Pantaleo as the officer who put Garner in the chokehold and said he had been placed on desk duty.

The Patrolmen's Benevolent Association blasted the move as "a completely unwarranted, knee-jerk reaction for political reasons and nothing more."

With Robert Brodsky

Get the latest news and more great videos at NewsdayTV Credit: Newsday

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Get the latest news and more great videos at NewsdayTV Credit: Newsday

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