But the two men disagree on whether the Black Lives Matter movement — a nationwide effort to bring attention to the deaths of people of color at the hands of police — is a force for good or causes harm to police.
Bratton, who spoke to WABC Radio's "Election Central with Rita Cosby" as part of a series of interviews with multiple news organizations over the weekend, said that the Black Lives Matter movement is attempting to portray all police officers as "racist or brutal or corrupt."
Bratton added that the effort "is attempting to portray the American police profession as hostile to blacks, which it is not. It is very heavily engaged in trying to protect blacks, whites, and Asians, and Hispanics."
De Blasio and first lady Chirlane McCray, delivered a different viewpoint Sunday on CNN's "New Day."
"I have a respect for the Black Lives Matter movement and I think that movement, just the very phrase Black Lives Matter, has changed the national discussion" about race, de Blasio said.
"We have a different perspective, that Black Lives Matter is a force for good," McCray added. "It's about peaceful protest. It's about about shining a light on the problems that we have in race relations across this country."
The difference of opinion comes in the wake of the shooting deaths Thursday of five police officers in Dallas during a peaceful protest of fatal police shootings of two black men, Alton Sterling in Baton Rouge, Louisiana, and Philando Castile in St. Paul, Minnesota.
De Blasio has expressed concern about the history of race relations in this country that has led to the shooting of so many black men at the hands of police while also highlighting the good work police do to keep New York City residents safe.
Last week, the mayor once again talked about how parents of children of color have to train their children to safely interact with police, as he has done with his own biracial son, but also called on protesters in New York City to "recognize the pain" of police.
Bratton said the Black Lives Matter movement is not going about things the right way.
"It is not engaging in dialogue, instead they're engaging in protests where there is a lot of yelling and screaming. Yelling and screaming doesn't resolve anything, doesn't solve anything," Bratton said.
Sitting next to Bratton during a press conference at One Police Plaza Monday, de Blasio reiterated that Blacks Lives Matter was bringing attention to the historical mistreatment of blacks in this country but also commended Bratton for going "right at race" during his career.
De Blasio said there are some protesters who are looking for trouble.
“There are people that come to disrupt. They come to provoke, they come to make violence, they come to denigrate police and I have only disdain for them.”
“But that’s a very small number,” he continued. “The vast majority of protestors are law abiding people. I think they’ve hit the right note. The very phrase (Black Lives Matter) has made us recognize that sadly our history do not value African-Americans.”
Bratton doubled down on his earlier comments, calling the Black Lives Matter movement’s agenda “a different type of bigotry.”
The commissioner said he only has a problem with protesters who antagonize police with their "poison talk" and that there needs to be more protests against the number of minorities who are shot by other minorities as well as against the flood of illegal guns that come into the city.
“The germ that allows racism to grow is the stereotype— the painting with a wide brush against a race, color or religion,” Bratton said, reading from a prepared statement. “When you have protestors who are claiming police are racist or that cops are cold-blooded killers, you have the same construct.”
“To call (police officers) racist or killers is to commit the same sin they’re protesting against,” he added.
In spite of their differences, de Blasio said he and Bratton are in "strategic unity" and that's one of the reasons crime in the city is low.