“I don’t think that anybody should be punished because of their race,” said Stewart, surrounded by about 20 mostly Vietnamese supporters inside the Eden Center, a Vietnamese American mall in Falls Church. “We know that quotas are illegal under the Constitution.”

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Stewart, chair of Prince William County’s board of supervisors, is nearly 20 percentage points behind Kaine in most polls, trails him badly in fundraising and is struggling to overcome controversies surrounding his past ties to white supremacists. In a purple state where President Trump is unpopular, Stewart has been running in the Trump mold and promoting a hard-line agenda against illegal immigration.

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His attack on the use of race in admissions follows a similar stance by the Trump administration that recasts a years-long battle against affirmative action as hurtful to Asian families.

In August, the Justice Department backed a group of Asian American students suing Harvard University over its admissions policies.

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The department argued that the school has failed to show that it does not unlawfully discriminate against Asian applicants in an admissions policy that uses race as one of several factors.

Harvard has said it does not discriminate against applicants from any group and argued that admissions policies that use race as a factor have been consistently upheld by the Supreme Court. It has been backed by the NAACP Legal Defense and Educational Fund, the American Civil Liberties Union, some economists, and social scientists and academics.

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The 2014 case, likely to be tried in October, could become the next test of whether the Supreme Court is willing to overturn decades of precedent and ban consideration of race in admissions. The high court has affirmed multiple times, most recently in 2016, that schools may take race into account as one factor among many in pursuit of assembling a diverse class, although it also placed limits on the practice.

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On Monday, Stewart sought to win more support over the issue, arguing that Asian students must often have better grades and higher standardized test scores than non-Asian students to gain entry to the same universities.

“Is it okay for universities to practice racial discrimination at the universities against kids?” Stewart asked the small crowd, eliciting shouts of “No!”

“Regardless of our skin color and the origin of our ancestors, my money is as good as yours . . . and my children’s SAT score is as meaningful as your children’s,” said Daniel Feng, board member of a conservative group called the Chinese American Alliance.

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Stewart also attacked Kaine, arguing that by supporting diversity programs, he is “okay with using race as a basis for keeping people out of our universities.”

Kaine’s campaign declined to comment.

A spokesman for the Democratic Party of Virginia accused Stewart of angling for more support from Asian Americans without any real plans to help students.