Hip-hop magnate Russell Simmons, joined by a group that wants to outlaw horse-drawn carriages in New York City, demonstrated growing impatience Thursday with Mayor Bill de Blasio's failure to fulfill his campaign promise of a ban.

The effort is stuck in the City Council, some of whose members have recoiled at aggressive tactics by horse-carriage foes. There was new friction after Simmons, in a winding soliloquy, compared what he calls animal abuse to slavery and the Holocaust.

"There were people for slavery ... There were people who put people in ovens," Simmons said when asked about council members supportive of the carriage industry.

Councilman David Greenfield (D-Brooklyn) in an interview called it "outrageous" to compare the plight of horses with the "worst genocide in modern history."

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Greenfield, undecided on the ban, added in a statement that Simmons "doesn't help his cause when he engages in outrageous hyperbole that minimizes the murder of much of my grandparents' family."

De Blasio had vowed as a candidate in 2013 and upon taking office to immediately shut down the "inhumane" carriage horse business. But in the year and half since he took office, there has been no resolution. A council bill to offer the 300 carriage drivers alternate employment behind the wheel of green taxis awaits environmental review, committee hearings and votes to pass the measure.