Dde Blasio said New York is proud to have supported the South African leader, who died Thursday.
Mandela's first stop on his 1990 U.S. visit was New York, where he was welcomed by Dinkins and de Blasio, then a mayoral aide. It was just months after his 27-year incarceration ended.
The mayor-elect said on Saturday that it's now up to New York to live in Mandela's spirit of economic and racial equality.
De Blasio says Mandela is the socially progressive model the city should follow.
The event also brought together Sharpton and Bratton, who was tapped this week by de Blasio to return to the role of police commissioner. His previous tenure ended nearly two decades ago.
Sharpton said New York cannot mourn the South African leader who fought for the constitutional rights of minorities - then have police "profile" young blacks.
Bratton told the mostly black audience at Sharpton's National Action Network that his commitment to the city is that "there will be freedom and equality for all" and the police will be "respectful."
A federal court ruling that ordered major reforms to the stop and frisk tactic is on hold pending an appeal. The ruling came after four minorities sued saying they were wrongly targeted by police.
Sharpton says he's worked with Bratton as both an ally and an adversary, and hopes they can work together on racial profiling and "to continue the decrease of violence and crime in our community."
de Blasio stressed that Bratton will try to continue the city's record public safety gains while improving police-community relations, which he said he believes have been strained by the police tactic known as stop and frisk.
The tactic allows police to stop anyone believed to be acting suspiciously. Its supporters say it has driven down crime while its critics say it unfairly targets black and Latino men.
"Bill Bratton knows that when it comes to stop and frisk it has to be used with respect and it has to be used properly," de Blasio said. "Public safety and respect for the public are not contradictory."