Pete Buttigieg is near the top of the polls in overwhelmingly white states like Iowa and New Hampshire, but he’s hearing questions from donors at his private fundraisers in the Bay Area about what he can do to attract more support from African American voters.

It is a question that hounds the 37-year-old mayor of South Bend, Ind. Nationally, Buttigieg is backed by just 2% of African Americans who are registered Democrats or lean Democratic, according to a Quinnipiac University survey released Monday. His support is at 13% among whites.

His lack of African American backing helps to explain why Buttigieg is mired in the single digits in the more racially and ethnically diverse early voting states, South Carolina and Nevada. The racial divide could ultimately doom Buttigieg’s campaign, as 1 in 4 Democratic voters is African American.

Buttigieg told supporters at a fundraiser Monday in Woodside that while he doesn’t put too much stock in polls, he was encouraged by African American voters who said they had yet to form an opinion of him. He pointed to a history of politicians reaching out to communities of color only in election years, saying it’s natural that someone new to the national scene would be slow to gain African American support.

“There’s a sense of skepticism (among nonwhite voters) that exists for various reasons,” Buttigieg said.

The Woodside stop was one of four Buttigieg fundraisers over two days in the Bay Area. He also held private events Monday in Palo Alto and San Francisco. On Sunday evening, Buttigieg appeared before 150 people at Hall Wines, a Sonoma County winery owned by Kathryn Hall, U.S. ambassador to Austria from 1998 to 2001, and her husband, Craig. Tickets ranged from $500 to $2,800.

There, Buttigieg was again asked how he would bolster his support in the African American community.

Buttigieg said African American voters in the South had been “abused” by the Republican Party and “taken for granted” by Democrats.

“When the new guy comes along promising all these great things and all these big plans, there is some very well-founded skepticism about whether you can actually deliver,” Buttigieg said. “Before anyone can explain what’s in your hands, you have to explain what’s in your heart.”

Buttigieg pointed to his recent travels to the South, saying he had engaged in listening sessions and conversations with African American leaders and voters in South Carolina and Alabama.

It will be an uphill battle for Buttigieg to win over African American leaders. Last month, the New York Times reported that Vice President Joe Biden, who polls show has the most support among black voters nationally, had been endorsed by 154 current or former African American or Latino elected officials. Buttigieg had been endorsed by only six.

Buttigieg said that building his support will take time, and that voters who have heard his plans tend to like them. In July, Buttigieg released “The Douglass Plan,” named after abolitionist Frederick Douglass, an 18-page document with policy prescriptions for policing, public health, education and voting rights.

“You can’t just delete a racist policy and replace it with a neutral one and expect equality to come about,” Buttigieg said.

The questions about Buttigieg’s nonwhite support come from a state that has been a deep mine of his financial support. California donors have accounted for 22% of the $51 million that Buttigieg has raised for his 2020 run, but that hasn’t translated into strength in state polls. He is running fourth in California with 12%, behind Vermont Sen. Bernie Sanders at 24%, Massachusetts Sen. Elizabeth Warren at 22% and Biden at 14%, according to a Berkeley IGS Poll.

Joe Garofoli is The San Francisco Chronicle’s senior political writer. Email: jgarofoli@sfchronicle.com Twitter: @joegarofoli