Storm Lake, Iowa — Pete Buttigieg warned Saturday that Senator Bernie Sanders runs the risk of alienating Republican and independent voters who might be open to voting for a Democratic presidential candidate because of concerns with President Trump.

"There are a lot of folks who are ready to consider voting Democrat for the first time in a long time. But I want to make sure that they feel welcome in that coalition we're building," he said in an interview with CBS News.

The wide-ranging conversation also included sharp criticism of the president's recent comments about U.S. military service members injured in Iraq, discussion of the rise of Mike Bloomberg, and how Buttigieg plans to continue seeking support from minorities.

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Buttigieg isn't far behind Sanders, and Joe Biden in the CBS News' newest Battleground Tracker poll released on Sunday of Democrats likely to participate in the Iowa caucus but is farther back in the 14 states holding contests on Super Tuesday. A New York Times/Siena College poll of Iowa Democrats released on Saturday also gave Sanders a lead.

Hours after the poll's release, Buttigieg's team sent two emails to supporters warning of Sanders' rise. One message said, "We can't risk going back to the same Washington playbook that's failed us in the past."

Buttigieg told CBS News he is seeking support in parts of Iowa where Sanders cannot by delivering his message in liberal and conservative counties to build a coalition of progressives, moderates and what he likes to call "future former Republicans."

"We're going into some of these counties that voted heavily for Trump, but are full of people who are just sick of what this president is doing," he said. "And part of how we demonstrate that I'll be the right candidate to beat him in the fall is to make sure that we're competing in rural and urban areas alike."

The interview took place in Storm Lake, the seat of Buena Vista County, which Mr. Trump won with nearly 59% of the vote in 2016.

Asked about former Secretary of State Hillary Clinton's recent comment that "nobody likes" Sanders on Capitol Hill, Buttigieg declined to weigh in on whether she's still relevant to the Democratic Party. However, he said, "The less 2020 resembles 2016, the better we are at a moment when we have got to recognize what we share as a party, the shared values that motivate us."

In the interview, the normally unflappable Buttigieg sharply admonished Mr. Trump for saying last week that service members enduring traumatic brain injuries after an Iranian missile attack into Iraq had suffered "headaches" and for reportedly disparaging senior military officers as "losers and babies" during a contentious 2017 meeting at the Pentagon.

"It makes my blood boil," said Buttigieg, a former Naval intelligence officer. "The president of the United States showing this level of disrespect to everybody from — remember these injured service members that he's talking about? He is their commander-in-chief right now. Their lives depend on his wisdom and judgment right now. And he can't even show a basic level of concern."

"Traumatic brain injury is life threatening, not just at the time, but for the rest of your life," he added. "It can completely debilitate somebody who has served this country. And for the president to belittle that kind of sacrifice, for the president — who avoided serving because he said bone spurs made it impossible for him to be able to do his part — to turn around and demean the experience of soldiers in harm's way who were injured, who were very concretely and literally injured by an Iranian missile attack is one more example of why Donald Trump has no business anywhere near the Situation Room."

While campaigning in four states on Friday, Buttigieg said he was able to reunite with a member of his old Naval intelligence unit who is preparing to deploy to Iraq.

"I don't want him to go to Iraq at a time when his own commander in chief is not willing to support those who are there," he said.

Regarding Bloomberg, Buttigieg said that he would like to see the former mayor more actively join the fray and participate in upcoming Democratic presidential debates.

"When you're competing for an office, you would want to be debating among everybody who has a shot. I think it's unfortunate if we don't have that kind of competition," he said. "Look, one of the best things about this early state process is that it forces us to get off of the airwaves and away from the ads and actually look people in the eye."

Bloomberg is skipping the first four Democratic presidential primaries in favor of competing for delegates in the Super Tuesday states. He is also declining campaign donations, making him ineligible to meet the party's fundraising thresholds and appear on a debate stage.

Asked how he would contrast himself with the 77-year-old former mayor of New York City, which has over 8.5 million residents, compared to South Bend's 102,000, the 38-year old Buttigieg said he considers the small size of the Indiana city he led as mayor to be an advantage.

"That's kind of the point," he said. "There's so many South Bends out there, many of them right here in Iowa."

Buttigieg also defended his current approach to winning support from minority voters, despite reams of data showing he is struggling to win favor among Asians, Blacks and Latinos. "We will continue with that all-of-the-above strategy to reach out to minority voters," he said.

While consistently polling in the top tier in Iowa and New Hampshire, Buttigieg continues to struggle especially among African-American voters. This has not escaped his notice. In a conversation with Democratic activist Angela Rye in South Carolina on Thursday, Buttigieg acknowledged that some of his rallies in South Carolina are filled with a mostly white audience.

"In order not just to win, in order to deserve to win, I've got to be speaking to everyone," Buttigieg told Rye.

In the CBS News interview, Buttigieg cited his conversation with Rye and several interviews with radio host Charlamagne tha God as "the right kind of engagement to make sure we have conversations that are just different from what you can do in a thousand-person rally. And we will continue with that."

But Buttigieg has had several missteps while seeking African-American support. Last weekend he rearranged his campaign schedule to attend Martin Luther King Jr. Day events in South Carolina amid criticism he would be skipping them to attend similar events in Indiana. Earlier in the cycle, the mayor's campaign had used a stock photo of a Kenyan woman on his campaign's website with his plan to end systemic racism in the U.S. And his complex relationship with law enforcement and minority communities in South Bend remains fodder for his critics.

Still, Buttigieg remains confident he will prevail.

"Every time my party's won in the last 50 years, it's been with a nominee who is new to national politics, had not run for president before, did not have an office in Washington, or at least hadn't had one for very long and was opening the door to a new generation of leadership," he said, adding later, "I'm here to lead America in turning the page."