Snyder mentioned William Henry "Lone Star" Dietz, the team's first coach whom the Redskins were named after to honor his "Native American heritage," and Walter "Blackie" Wetzel, a former president of the National Congress of American Indians and chairman of the Blackfeet Nation, who helped design and approve the team's logo as examples of the positive history of the nickname.
"It's just historical truths, and I'd like them to understand, as I think most do, that the name really means honor, respect," Snyder told ESPN's John Barr.
"We sing 'Hail to the Redskins.' We don't say hurt anybody. We say 'Hail to the Redskins. Braves on the warpath. Fight for old D.C.' We only sing it when we score touchdowns.
"That's the problem because last season we didn't sing it quite enough as we would've liked to," Snyder said with a laugh.
Barr also asked Snyder, what is a Redskin?
"A Redskin is a football player. A Redskin is our fans. The Washington Redskins fan base represents honor, represents respect, represents pride. Hopefully winning," Snyder said. "And, and, it, it's a positive. Taken out of context, you can take things out of context all over the place. But in this particular case, it is what it is. It's very obvious."
In June, the United States Patent and Trademark Office canceled the team's trademarks in a 2-1 ruling on the basis they are "disparaging to Native Americans." The team has appealed the ruling and has said it is confident it will be overturned.
Several politicians have called on Snyder to change the team's name, including Attorney General Eric Holder, Sen. Harry Reid and former Secretary of State Hillary Rodham Clinton. President Barack Obama said last year that if he owned the Redskins, "I'd think about changing [the name]."
On Tuesday, Maryland Gov. Martin O'Malley said on his Facebook page that it is "probably time" for the Redskins to change the nickname. The team plays in Landover, Maryland, at FedEx Field.
The Democratic governor, who is mulling running for president, posted: "I was asked earlier today and answered that I do believe it is probably time for the Washington Redskins to change their team name.''
NFL commissioner Roger Goodell has not pressured Snyder to change the name and has said he stands by his stance that the name honors Native Americans.
Snyder's full interview will air in an "Outside the Lines" special Sept. 2 on ESPN2 at 8 p.m. ET.
The Associated Press contributed to this report.
Snyder Speaks On Nickname Controversy
Washington Redskins owner Dan Snyder shares his thoughts with "Outside the Lines" on the controversy over the team's nickname.