"It gives me hope that as a nation and as a people, we're going to get there,'' Lewis told Al Roker on the 3rd hour of TODAY Thursday. "We're going to make it. We're going to survive, and there will be no turning back.
"There may be some setbacks, there may be people who will stand in our way, but we will not go back. We've come too far, and we're not going to give up now."
Lewis, 80, is a 33-year member of the House of Representatives from Georgia who previously was a leader of the civil rights movement in the 1960s and frequently marched alongside Martin Luther King Jr.
A documentary about his activism called "John Lewis: Good Trouble" is set to be released on July 3 on streaming platforms.
"Dr. Martin Luther King Jr. would be very pleased and very proud of seeing so many people, hundreds, thousands, millions, engage in nonviolent protests all over America but around the world," Lewis said. "He's looking down and he's saying to each and every one of us, 'Keep it up, and never give up, never give in, but to keep the faith and to keep your eyes on the prize.'''
Floyd died on May 25 after former Minneapolis police officer Derek Chauvin was filmed kneeling on his neck for nearly nine minutes as he pleaded for his life. Chauvin's charges were upgraded from third-degree murder to second-degree murder on Wednesday, and three other officers who were involved in the incident were charged with aiding and abetting murder.
"For one, I was very pleased to see the changes in the charges," Lewis said. "It will send a strong and powerful message that you will not just go out and kill a person and know that you're killing that person without powerful action on the part of the law of the land."
"(Floyd's death) made me so sad. It made me cry to see what was happening to this person of color, but to any human being. I think it sends a message that we will not give up on justice, we will not give up on fairness, that we will continue to press, and press on for what is right, for what is fair, for what is just."
Lewis also reflected on Tuesday's incident in which police used tear gas on peaceful protesters outside the White House to clear the way for President Donald Trump to stage a photo op in front of St. John's Episcopal Church while holding a Bible. He has openly clashed with Trump in the past, including saying he is "not a legitimate president" in 2017.
"It made me sad, really, really truly sad to see what was happening,'' he said about the incident. "Here in America, people tried to exercise their constitutional right, and to see the president be part of an effort to take away from people a simple constitutional right, the right to protest.
"Dr. King used to say we have a right to protest for what is right, and we did it in a peaceful, orderly and nonviolent fashion, and that's what people must be allowed to do today."
Lewis, who is being treated for pancreatic cancer, also gave an update on his health.
"I'm feeling pretty good," he said. "I'm doing well, obeying my doctor and nurses, and with the help of the American people and health providers, I believe we will pull through."