The police commissioner has seen his numbers drop 9 points since June, while the mayor's remained flat.
The mayor campaigned against abusive police practices, but is also looking to back the NYPD.
Challenger state Sen. Adriano Espaillat refused to concede until all votes were counted.
The move is the latest in the escalating endorsement race between Rangel and Adriano Espaillat.
Charles Rangel ignored the needs of East Harlem in favor of Central Harlem, Espaillat supporters said.
Charles Rangel, 83, won his 2012 primary by fewer than 1,000 votes.
Melissa Mark-Viverito and Inez Dickens are positioning themselves for City Council Speaker.
The Harlem City Council race got dirty as fliers called Inez Dickens a "slumlord millionaire."
Charges may hurt black and Latino elected officials seeking to increase their numbers and gain clout.
City Council Speaker Christine Quinn has become a near-constant presence uptown this summer.
After a second hard-fought primary victory, many in Harlem say Charles Rangel can leave on his own terms.
Despite ethics charges and an anti-government mood, Harlem voters remain loyal to their congressman.
Challenger Adam Clayton Powell said Rep. Charles Rangel has lost his power and support at a forum on Monday night.
Joyce Johnson accused Charles Rangel of avoiding questions from his challengers.
Smikle said, "I’m running as an insurgent, the outsider.”
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