“This time, we don’t want to focus on the negativity,” said Ms. Stein, who attended Ms. Harris’s rally on Friday in Charleston. She said she felt that the talk of Ms. Warren’s Native ancestry was driven by Mr. Trump.

“He’s just so loud and gets people to focus on whatever he says,” Ms. Stein added.

It was Ms. Warren who decided last year to highlight the ancestry issue, by giving interviews that repeatedly defended her family’s story that they originated from Cherokee and Delaware tribes and by taking a DNA test that showed strong evidence that she has Native American pedigree “6-10 generations ago,” according to results released by Ms. Warren’s office. After some Native leaders said she dishonored tribal governments and citizens by using the DNA test to assert her own ancestry claims, and some critics on the left said that the test played into Mr. Trump’s hands, Ms. Warren apologized multiple times this month for calling herself Native American for years.

Whether the ancestry issue could be a problem for Ms. Warren with general election voters if she won the Democratic nomination is unclear at this early stage. For now, the issue has become a familiar narrative among Washington insiders: Republican Party officials are trying to brand her as inauthentic, and some liberal activists have expressed dismay with her approach to the whole issue. Most painfully for Ms. Warren, some prominent Native Americans have soured on her, saying she exhibited unforgivable behavior consistent with cultural appropriation. (Other Native leaders have been more supportive.)

[Check out the Democratic field with our candidate tracker.]

Ms. Warren may well face new questions about the extent of her Native claims. But criticism of her has been cooling in some quarters recently, after Ms. Warren’s apologies and her steps to consult privately with prominent critics to understand their concerns.

Ms. Warren briefly appeared at the National Indian Women Honor luncheon last week in Washington to support a Native leader from Massachusetts, who was winning an award. She is also working on legislation with Representative Deb Haaland, the New Mexico Democrat who last year became one of the first Native American women to serve in Congress; it would seek to address funding shortfalls in tribal lands.

Julian Brave Noisecat, a Native American journalist and activist who has criticized Ms. Warren previously, said: “Based on my conversations with tribal leaders and advocates, the consensus position is that she’s one of the strongest allies of Indian country in Congress. She has good relationships with tribes across the board. And I think that’s relevant.”

Mr. Noisecat said the ancestry matter had become double-edged: More than any other Democratic presidential candidate, Ms. Warren has caused the most upset among Native American communities, but has also probably done the most outreach and is more vocal on issues that effect tribal citizens than other presidential candidates.