Washington (CNN) 2020 Democratic hopeful Pete Buttigieg affirmed his belief in capitalism on Tuesday but suggested that the US economic system has let a lot of Americans down and called for greater "fairness."

The comments come amid a heated debate among Democrats and progressives over whether the party should more openly embrace socialist policies in the age of Donald Trump.

"I think the reason we're having this argument over socialism and capitalism is that capitalism has let a lot of people down," the South Bend, Indiana, mayor said in an interview with CNN's Poppy Harlow and John Avlon on "New Day."

Buttigieg reiterated that he believes in "democratic capitalism." He expressed alarm over previous comments Stephen Moore, the President's nominee for the Federal Reserve Board of Governors, made that recently surfaced in which Moore said he believed capitalism was more important than democracy.

"I would say the reverse ought to be true -- that at the end of the day, we prioritize democracy," Buttigieg told CNN on Tuesday. "And having that framework of a rule of law, of fairness, is actually what it takes for markets to work."

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