a large-scale poll conducted annually, found in July that Asian Americans leaned toward supporting Democratic congressional candidates by a margin of 54 percent to 27 percent. Those voters trusted Democrats more than Republicans on issues including guns, the environment and race — but split evenly on which party they preferred to handle the economy.

Mr. Trump remained intensely unpopular with Asian American voters.

EunSook Lee, the head of the AAPI Civic Engagement Fund, a progressive nonprofit, said Democrats still had a window to solidify their political relationship with the Asian American electorate.

Of Asian American voters, she said, “They care about reproductive rights. They care about gun control. And on all those issues, the Republican Party isn’t budging.”

In a real estate office in Duluth, Ga., minutes away from Johns Creek, Mr. Reddy — Dr. Au’s Republican opponent — gave a blunt assessment of his party’s efforts to court Asian Americans: “Still not there.”

Mr. Reddy’s office is all but wallpapered with photos of himself with Republican politicians like George W. Bush and Mitt Romney, an expression of his personal devotion to the G.O.P. But Mr. Reddy, 71, said most of his Indian American friends saw the Republican Party as “all white.”

“That’s the only popular perception,” he said. “And there is truth to it, actually.”

The party, he said, had been harmed by episodes like a rally at the end of the Georgia Senate runoffs when Senator David Perdue, a Republican incumbent, had mocked the pronunciation of Ms. Harris’s first name. National Democratic organizations, including the advocacy group Indian American Impact, mounted a fierce campaign targeting Asian American voters with information about Mr. Perdue’s insulting conduct.

The G.O.P.’s business-friendly economic agenda could resonate in the community, Mr. Reddy argued, but Republicans were still seen as “anti-immigrant” and overly tied to Mr. Trump. A supporter of Mr. Trump for years, Mr. Reddy said it had grown difficult to justify his behavior.

Republicans in Georgia have taken something of a divide-and-conquer approach to the Asian American vote. The governor appointed the first Asian American justice to Georgia’s Supreme Court and Republicans have recruited a few Asian American candidates to run in state legislative seats.

At the same time, the Republican-dominated legislature has used gerrymandering to break up ethnically Asian communities and mute their influence at the polls. Dr. Au became a victim of that strategy last year when Republicans demolished her State Senate district, prompting her to run for a Democratic-leaning seat in the lower chamber instead.

Mr. Tran, the businessman who introduced Mr. Biden last year in Atlanta, is now a Democratic candidate for the state legislature in a district with a large community of Asian American voters. Mr. Tran, 46, said he often found voters expressing unease about left-wing ideas on police reform.

He said he had encountered pervasive concern about gun violence and Republican support for lax firearm laws.

“Everyone is scared to death about guns,” Mr. Tran said. “I was eating dim sum and the waiters were saying, ‘We can’t stop looking at the door and wondering if the next person who comes in will have a gun.’”

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