The collection of legislation would make it illegal for a police officer to use a choke hold or any action that restricts breathing, and it would also create a "disciplinary matrix" to detail the appropriate penalty ranges for officers and provide more transparency regarding internal discipline.
"The eyes of the world are on New York City, and it is time for us to lead," Johnson said.
Sharpton praised peaceful protesters but also condemned those who would use the tragedy as cover for anarchy, urging them not to pretend they are activists by using Floyd's name. He was also critical of the federal response to the crisis.
"They are trying to militarize the country rather than humanize the country," Sharpton said.
He said the nation is right to be outraged, and that the bills on the table can be the first step in real change.
"These bill can be the real focus of where this nation can go, this can be the example New York can set nationwide," he said. "New York should set the tone, because the first time we heard, 'I can't breathe,' it was not in Minneapolis. It was on Staten Island, six years ago, and we did nothing."
Carr said she has been fighting for such reforms for years, ever since her son was killed.
"New York, stand up and stop these killings" she said.
She was also critical of those stoking violence.
"The country is in an uproar," she said. "And a lot of it is just opportunists. We ask the opportunists to go away. This is our movie, and we don't want to be an extra in our movie."
Still, she urged for continued demonstrations.
"The protests must go on, because we've got to wake up America," she said. "We all live in the same house, but we are treated differently."
Activists hoped the passage of the bills could serve as the basis for new laws at the federal level.
"We will never forget Eric and the systematic racism and injustice that stole him from you and our city," Johnson said. "That is why I am here today, to listen and to take action."
The City Council is expected to vote on both bills later this month.
Monday coverage of protests and looting in NYC
NYPD officers attacked amid looting, violence in Bronx
Video shows dramatic post-looting damage in Bronx
Floyd Mayweather will pay for George Floyd's funeral
Multiple police officers injured when protests turned violent in 2 cities
Manhattan stores hit by looters
In moving show of support, one of NYC's top cops takes a knee, hugs George Floyd protesters
Calls for change at peaceful George Floyd protests in Brooklyn
SoHo like a war zone after looters go on rampage
Search for vandals who spray painted St. Patrick's Cathedral
President Trump takes shelter in White House bunker
Mayor de Blasio's daughter arrested during protests in NYC
Sunday's protests largely peaceful until night came
NYPD vehicle drives into group of Brooklyn protesters
Video shows NYPD officer shoving woman to ground during Floyd protests
PHOTOS: George Floyd protests erupt into violence in NYC
Minneapolis Park Police release bodycam footage near George Floyd's in-custody death
3 people, including Catskills woman, face federal charges in Molotov police attacks: source
Brooklyn protests: Calls for review of violent protests, police response; hundreds arrested
1 federal officer killed, 1 critically hurt near California protest in 'act of domestic terrorism'
Derek Chauvin, police officer accused in George Floyd's death, charged with murder
Mayor de Blasio urges protesters to remain peaceful, socially distant
* More New York City news
* Send us a news tip
* Download the abc7NY app for breaking news alerts