New York Mayor Bill de Blasio on Sunday admonished former Mayor Rudy Giuliani for his repeated recent comments that "responsibility is on the black community" for reducing the necessity of police officers in their communities.

"I think he fundamentally misunderstands the reality," said de Blasio on ABC's This Week. "There is a problem here. There is a rift here that has to be overcome. You cannot look at the incident in Missouri; another incident in Cleveland, Ohio; and another incident in New York City all happening in the space of weeks and act like there's not a problem."

"There's something fundamental we have to get at here," de Blasio said, adding, "And it's not going to be helped by accusing either the community or the police of having bad intention or not doing their job. In fact, I think everyone is trying to do their job."

De Blasio's comments come at the end of a week of protests sparked by the decision of a grand jury not to indict the New York police officer responsible for the death of Eric Garner on Staten Island.

"I make it a point not to talk about any element of the judicial process per se," said de Blasio. "I'd talk about what we have to do to fix the relationship between police and the community... As an executive in public service, I think it's important to respect the judicial process."

When asked about comments he made earlier in the week about how he and his wife "had to literally train" their son Dante how to handle encounters with police (for which the head of the police union said he "threw cops under the bus"), de Blasio said there was "so much misunderstanding" about what he said.

"What parents have done for decades, who have children of color, especially young men of color, is train them to be very careful when they have a connection with a police officer," de Blasio said.

"It's different for a white child. That's just the reality in this country," de Blasio said. "And with Dante, very early on with my son, we said, look, if a police officer stops you, do everything he tells you to do, don't move suddenly, don't reach for your cell phone, because we knew, sadly, there's a greater chance it might be misinterpreted if it was a young man of color."

"I'm just saying what people are actually experiencing and have been for decades," de Blasio said. "I've talked to a lot of families of color, well before this time, because I've said things like this before. And they've said to me over and over and over again that they appreciate someone finally acknowledging that they have that conversation with their sons. It's a painful conversation. You can sense there's a contradiction in that conversation."