Four emergency medical services workers employed by the Richmond University Medical Center -- where a Staten Island man was pronounced dead Thursday after NYPD officers put him in a chokehold -- were placed on modified desk duty as part of an investigation into response times, an FDNY official close to the probe said Sunday.

The workers, who were not identified by name, cannot respond to 911 calls, the official said.

An officer seen on amateur video putting Eric Garner, 43, into a banned chokehold -- identified as Daniel Pantaleo, an eight-year NYPD veteran -- was placed on modified duty, which in his case means being put on desk duty and also having his badge and gun taken away, police said Saturday. A second officer at the scene, who was not identified, was placed on desk duty but will still have his gun and badge, police said.

Representatives of Richmond University Medical Center in Staten Island did not respond to requests for comment.

The Rev. Al Sharpton, meanwhile, kept pressure Sunday on city officials to investigate the first responders at the scene of the confrontation with Garner, arrested on the suspicion of illegally selling individual, untaxed cigarettes. Sharpton, taking the pulpit at the historic Riverside Church in Manhattan, called other faith leaders to action.

He also asked why, according to the video footage, police officers involved continued to pin Garner down and keep him in a chokehold as Garner repeatedly gasped, "I can't breathe."

"Even if police procedure doesn't kick in, when does your sense of humanity kick in?" Sharpton said.

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Mayor Bill de Blasio -- who postponed his family vacation in Italy by one day to handle fallout from Garner's death, eventually leaving Saturday evening -- told reporters upon his arrival in Rome Sunday that he believes Staten Island officials handled the situation well "in a very difficult circumstance," communicating with the community.

He also emphasized that a "thorough investigation" is being conducted.

De Blasio was briefed by senior administration officials in the morning on the NYPD investigation into Garner's death and "continued engagement with community leaders, elected officials and clergy members," his office said.

Sharpton said Garner's widow and mother are "trying to be strong, but this is devastating" and are preparing for his funeral Wednesday in Brooklyn.

No determination has yet been made into the "cause and matter" of Garner's death, city Office of the Chief Medical Examiner spokeswoman Julie Bolcer said.

Richard D. Emery, chairman of the city Civilian Complaint Review Board, over the weekend announced a new study into more than 1,000 chokehold complaints received in the past five years.

With Alison Fox