Former Mayor Rudy Giuliani "fundamentally misunderstands the reality," New York City Mayor Bill de Blasio said today on "This Week" in response to Giuliani's recent comments focusing on violence within African-American communities, rather than questions over police interactions with minorities that have sparked nationwide protests.

"I think he fundamentally misunderstands the reality," de Blasio told ABC News chief anchor George Stephanopoulos in his first television interview since a New York grand jury decided this week not to indict police officers in the July death of Eric Garner in Staten Island. "We're trying to bring police and community together. 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," de Blasio added.

De Blasio was responding to comments made by Giuliani on Fox News last Sunday in which he said, "I think just as much, if not more, responsibility is on the black community to reduce the reason why the police officers are assigned in such large numbers to the black community. It's because blacks commit murder eight times more per capita than any other group in our society."

Giuliani, who had strained relations with many black New Yorkers during his tenure as mayor from 1994 to 2001, later said in separate comments that de Blasio's response to the Garner case this week contributed to tearing down respect for the criminal justice system.

Read: Four Fast Facts About New York Mayor Bill de Blasio

In an emotionally fueled news conference earlier this week, the mayor, who is married to an African-American woman and has a biracial son, Dante, discussed the precautions his son takes in interactions with police. Stephanopoulos asked the mayor Sunday whether he thought his son was at risk from his own police department.

"It's different for a white child. That's just the reality in this country," de Blasio responded on "This Week." "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."

"We all want to look up to figures of authority. And everyone knows the police protect us," de Blasio added. "But there's that fear that there could be that one moment of misunderstanding with a young man of color and that young man may never come back."

WATCH: New York City Mayor Bill De Blasio's Personal Reaction to Eric Garner Case

De Blasio denied that police had been "thrown under the bus" by his recent comments, as a New York City police union official asserted last week. The mayor said Sunday he has "immense respect" for those who serve in law enforcement, and that his city can "transcend" problems of bias between police and minority communities through improved training and communication.

"The point here is we have a whole series of things we have to do to change the dynamics in our city. This is true all over the country," de Blasio said. "We have to retrain police forces in how to work with communities differently. We have to work on things like body cameras that will provide a different level of transparency and accountability. This is something systemic. And we bluntly have to talk about the historic racial dynamics that underlie this."

"This is something our commissioner Bill Bratton is fundamentally a believer in, that if you train the police in a different approach to the use of force, in a different approach to communication with the community, a different approach to building relationships with the community, you won't see these tragedies," he added.

Earlier in the conversation on "This Week," the mayor said he respected the "process" when asked by Stephanopoulos whether he respected the grand jury's decision in Garner's death.

De Blasio on Democratic Losses in 2014

During his interview on "This Week," de Blasio also offered an explanation for why the Democratic Party took a large hit this year in midterm elections, saying the party did not directly enough address issues of economic inequality.

"In the 2014 cycle, Democrats did not speak bluntly about it," he said. "They did not honestly say to the people of this country, here's a crisis and we're going to do very specific things about it. We're going to be willing to take on those who are wealthy and ask them to do their fair share. We're going to be willing to take on corporations that are not being fair to their workers.

"If the people of this country heard Democrats enunciate a clear vision for economic fairness, I think you would have seen a very different result in 2014," he added.

The mayor, who ran former Secretary of State Hillary Clinton's 2000 Senate campaign in New York, offered praise for the potential 2016 presidential candidate, but reiterated that Democrats have to be "blunt" about economic issues in the next election.

"I think the world of Hillary Clinton. I think she's an extraordinarily capable person," de Blasio said. "I would say this to all Democrats running for any office - that we have to talk about economic reality and we have to talk about economic fairness… How are they going to believe we're going to fix anything if we're not blunt about the problem?"

Like "This Week" on Facebook here. You can also follow the show on Twitter here. Go here to find out when "This Week" is on in your area.