The latest development comes following a report in the New York Times claiming the administration is seeking Caban's resignation.
Caban appeared in public Monday night amid a federal investigation threatening to engulf the highest echelons of the NYPD.
Despite the investigation, Adams seems determined to prevail and planned to maintain a full schedule of public events this week until he tested positive for COVID-19 on Monday.
"Still working hard for the city here in Gracie Mansion," Adams said in a video posted to social media. "I remember when I got COVID at the beginning of my term, we continued to work and push through, we're going to do it again. Just wanted to let you know, take care."
The mayor acknowledged the rumors swirling around Caban stepping down, but said "there was nothing that came from me that fed those rumors at all."
"I don't think anything in life is guaranteed. I will say this, when I chose Eddie, I chose him for his experience and what he brought after 30 something years of service," Adams said. "Rumors are always out there, you can never keep up with the rumors that you hear."
Growing calls for NYPD commissioner to step down amid FBI probe into Adams administration
But Caban has lost the support of the city's most influential business group, the Partnership for New York City.
"The business community is confident the mayor will take the actions necessary to remove the cloud that this investigation has put over the police department," the business group said in a statement.
Caban was named commissioner of the NYPD just a little more than a year ago. Eyewitness News has learned his brother is accused of trying to leverage their relationship in order to get work providing security to nightclubs.
The commissioner has not commented publicly, but several New York City Councilmembers are demanding that he resign, saying a police commissioner forced to surrender his electronics creates an appearance that is disturbing enough that he should resign simply because of that.
"It's a very different world when you are the head law enforcement officer," said Queens Councilmember Robert Holden. "So, if there's a shadow over you it casts a shadow over the whole department."
Holden is urging Caban to step down.
"If there's some cronyism going on within the NYPD, that's got to be weeded-out. And, hopefully, the feds do that," he said.
Brooklyn Councilmember Lincoln Restler also believes Caban should resign.
"If the head of the NYPD is under investigation by the FBI, it's impossible for those agencies to work together in the ways that they should to prevent violent crime and keep us safe," Restler said.
It is just one of four federal investigations now focused on the NYPD and City Hall.
Federal agents on Wednesday took devices from Caban as well as Mayor Eric Adams' schools chancellor, two deputy mayors and several other advisers.
Sources say it's all part of a federal investigation into potential influence peddling in the Adams administration.
None of the officials involved have been charged with a crime, but the wave of searches added to a cloud of suspicion around Adams, a former city police captain who has fashioned himself as a champion of law and order.
They've also raised questions internally about the administration's ability to stay focused on serving the nation's largest city.
The seizures came nearly a year after federal agents seized Adams' phones and iPad as he was leaving an event in Manhattan. Investigators also searched the homes of a top Adams campaign fundraiser and a member of his administration's international affairs office.
In February, federal authorities searched two properties belonging to his director of Asian affairs as part of a separate investigation overseen by the U.S. attorney's office in Brooklyn.
Then earlier this summer, Adams, his campaign and City Hall all received subpoenas from federal prosecutors requesting information about the mayor's overseas travel and potential connections to the Turkish government.
(The Associated Press contributed to this report.)
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