Buttigieg, who edged out Senator Bernie Sanders in the Iowa caucuses and placed a close second to him the New Hampshire primary this month, said there is "no comparison" between Bloomberg's alleged behaviour and the way US President Donald Trump has treated women and people of colour.
But he sought to draw a contrast between Republicans and Democrats, arguing that "we in our party hold ourselves to the highest standard."
"It is going to be critical for us to have a nominee who can authentically lead and who can show growth on these challenges," Buttigieg said.
Senator Amy Klobuchar, another leading 2020 presidential contender, took aim at Bloomberg's record, particularly on stop-and-frisk, describing the former mayor's actions as "unconstitutional."
"I'll say this: I am on your show right now, Margaret, answering these tough questions," Klobuchar told host Margaret Brennan on CBS News. "Where is he? He just keeps running a bunch of ads. He'll probably have more ads during your show in certain states than I'm on answering your questions. I think he cannot hide behind the airwaves and the money."
Former Vice-President Joe Biden, who has struggled for traction after his disappointing performances in Iowa and New Hampshire, also criticised Bloomberg. In an appearance on NBC News, Biden said that "US$60 billion can buy you a lot of advertising, but it can't erase your record."
"You take a look at the stop-and-frisk proposals," Biden said. "You take a look at his ideas on redlining he's talking about. You take a look at what he's done relative to the African American community. I'm anxious to debate Michael on the issues relating to, you know, what we're going to face in Super Tuesday."
Bloomberg is skipping the first four states in the Democratic nominating process but has spent hundreds of millions of dollars on advertising across the country ahead of the March 4 Super Tuesday contests.
According to the 2015 audio, Bloomberg told an audience at an Aspen Institute event that "the way you get the guns out of the kids' hands is to throw 'em against the wall and frisk 'em."
As audio of the speech recirculated, Bloomberg's campaign last week released a statement in which the former mayor said that he had "inherited the police practice of stop-and-frisk, and as part of our effort to stop gun violence it was overused."
"By the time I left office, I cut it back by 95 per cent, but I should've done it faster and sooner," Bloomberg said in the statement. "I regret that, and I have apologised - and I have taken responsibility for taking too long to understand the impact it had on black and Latino communities."
Among the lawsuits that have been filed against Bloomberg over his behaviour towards women, the most high-profile case involved a former saleswoman. She sued Bloomberg personally, as well as his company, alleging workplace discrimination. She alleged Bloomberg told her to "kill it" when he learned she was pregnant.
Bloomberg has denied her allegation under oath, and he reached a confidential settlement with the saleswoman.
Yesterday, he tweeted in defence of his treatment of women throughout his career.
"I would not be where I am today without the talented women around me," he said. "I've depended on their leadership, their advice and their contributions. As I've demonstrated throughout my career, I will always be a champion for women in the workplace."