De Blasio and host Tucker Carlson also sparred over the subject of mandatory firearm buybacks during his interview Thursday on "Tucker Carlson Tonight."
"I've said very clearly my goal is to get into those next debates -- and that's a month away until that cut-off period," he said. "I'm going to put ideas out there that I think are going to be meaningful for people. Even a $1 donation helps me to get into the next debates."
During the interview, De Blasio also said he and Carlson agree that automation in the workplace threatens the future of American jobs.
"Presenting ideas like this that actually could change things for working people -- I think the more I get out there with that, the more chances are that I can get into these October debates," he said.
The New Yorker added that his experience running America's largest city is a good grounding for the skills needed to execute the office of the presidency.
He cited what he considered "real, serious foundational changes" in New York and likened his current role to that of a chief executive.
"I'm able to, as a CEO, keep making sure my agencies are doing their jobs. That's actually what qualifies you to be president of the United States -- that you know how to run something as big and complex as this city."
Regarding the policy of mandatory firearm buybacks -- an idea floated by gun control advocates in the wake of recent mass shootings -- de Blasio said military-style weapons have no place in the hands of civilians.
"We've got to end the availability of assault weapons in this country," he said.
"I think that if there was a ban on assault weapons and there was a buyback program, the vast majority of people would do the smart thing and they would sell them back."
Carlson pressed the mayor on how he would react to citizens who would refuse law enforcement orders to surrender their rifles, adding that some weapons used to hunt game would qualify under some specifications for "assault weapons."
"You would have, unfortunately, tragically ... cases of violence," Carlson said.
De Blasio said Carlson made an important point that would have to be dealt with in a responsible way.
"We cannot have assault weapons in our society. We've seen the devastating impact, they need to be banned. And that means, by definition, you don't leave millions and millions of them out there. The buyback is the obvious approach," he said, adding that pushback from gun owners would be "something we have to resolve going forward."
"Under the Second Amendment, there are going to be plenty of appropriate weapons that people can use for self-defense for hunting, if they're sportsmen, if they're marksmen ... but the military-grade assault weapons -- those just don't belong in the hands of everyday people."