FRESNO, Calif. — Pete Buttigieg, at a fundraiser over the weekend, acknowledged having fallen short in the past in demonstrating his commitment to African Americans, offering some of his most candid reflections to date on the challenge he faces in trying to win over a key Democratic constituency that has been slow to support his presidential campaign.

Buttigieg said that while he’s been building a campaign team that reflects his commitment to diversity, “I know that’s just the beginning.”

The mayor of South Bend, Indiana, went on to tell the story of an activist he met with in his office’s conference room early in his term who told him, “We don’t feel like we have a seat at the table.”

“He literally said this while literally sitting at my table,” Buttigieg said at the fundraiser in San Francisco, where Democrats had gathered for the party's California state convention. “I thought, what are you doing? You’re literally at my table. Well, if you’re in my office and at my table and you don’t feel like you have a seat at the table, what does that say about us?”

“Does that mean we may have sent out an invitation, but it doesn’t mean you feel welcome?" he said. "And so making sure that not just our personnel but our practices reflect that good will is, I think, particularly important for communities that have seen Democratic and Republican politicians let them down.”

NBC News obtained a recording of Buttigieg’s remarks at the fundraiser, which was closed to the press, from an individual who attended. The fundraiser took place at San Francisco’s National LGBTQ Center for the Arts.

Buttigieg said that while he’s already made clear his values as a candidate, “there’s a lot that can be shaped in terms of priorities and vocabulary and conduct and tone.” He asked donors supporting him “and anybody else who is focused on this and cares about this to feed back at us how we can make sure we’re doing this right.”

“Even as you can establish a groove, a level of good will, that won’t be quite enough because people are looking for results,” Buttigieg said.

Securing support from African American voters has become a key litmus test for all the Democratic candidates in the 2020 race, in which several black candidates are running and many Democrats — still bruised from Hillary Clinton’s defeat — are still eager to break more barriers to elected office.

Buttigieg is often asked on the campaign trail about whether he’s struggling to win over minorities, and usually describes his efforts to diversify his campaign and reach out proactively to voters of color rather than waiting for them to discover him. But in public, he rarely discusses his challenge with as much candor as he did at the fundraiser.

At a town hall Monday night on MSNBC, Buttigieg was asked what steps he could take to attract more support from black voters. “I think the biggest is that we've got to reach out in communities that haven't had a chance to get to know me,” he said.

“If you are neither already famous with a long track record in national politics nor yourself from a community of color ... it's going to take longer for people to come to know and trust you," he said. "We were able to do it in South Bend. The minority voters who know me best — by the way, not everybody, of course, but the voters who know me best contributed" to his re-election. But, he noted, “I had years to build up that kind of trust.”

As questions persist about the relatively few supporters of color among the packed crowds at his rallies across the country, Buttigieg has made a point to fill the top echelons of his campaign staff with women, Hispanics, people with disabilities, people of color, and those who are LGBT. If elected, Buttigieg himself would break a major barrier as the first openly gay president.

Describing “patterns of racial justice” in the nation's health care and criminal justice systems, the two-term mayor told donors he needs to “make sure I have a chance to explain what we did about this in South Bend.”

He cited his efforts to extend the economic recovery to black neighborhoods, to prevent displacement of black residents through the city’s “Home Repair” initiative, and to ensure an African American majority on the board that oversees policing decisions in South Bend.

“I want to make sure that record is understood,” Buttigieg said.