Pedestrians pass Memorial Church on the campus of Harvard University in Cambridge, Mass. (Steven Senne/AP)

A group opposed to racial preferences in college admissions Monday rejected Harvard University’s argument that it lacks legal grounds to sue the school over alleged discrimination against Asian Americans. The group said its lawsuit has unearthed “powerful evidence” that the university is violating Supreme Court guidance on the use of race in choosing a freshman class.

Students for Fair Admissions, based in Arlington, Va., asserted in a brief filed in federal court in Boston that it has legitimate standing as a plaintiff and that Harvard is seeking to divert attention from the core issue in the lawsuit — the group’s allegation that the elite university intentionally discriminates against Asian Americans, tilting admissions in favor of other applicants. Harvard, which denies the accusation, filed its latest arguments Friday.

Both sides, citing dueling analyses of admission data, are asking the judge to rule in their favor before a trial scheduled in October. The plaintiff derided Harvard’s bid for summary judgment.

“Harvard is — at best — hanging on by a thread,” Students for Fair Admissions wrote. “Even if Harvard somehow survives to a trial, it faces a steep uphill battle.”

The lawsuit, filed in 2014, represents the latest challenge to affirmative action in higher education. The Supreme Court has repeatedly upheld the use of race in admissions, within certain limits. Colleges are not permitted to use racial quotas, and they must also consider race-neutral measures to achieve campus diversity. But the high court has allowed selective colleges to consider race as one of many factors in what admissions officers describe as “holistic” review.

Foes of affirmative action want the Supreme Court to revisit the issue after a justice is seated to replace the retiring Justice Anthony M. Kennedy. But higher-education leaders are hoping to preserve the status quo.

Sixteen other selective universities filed a legal brief supporting Harvard’s position. Among them are George Washington, Johns Hopkins, Duke and Stanford universities, and all seven of Harvard’s peers in the Ivy League. These universities said a diverse student body is essential to the educational experience. Like Harvard, they said they consider race as one factor among many in the background of their applicants. They rejected the argument that race should be excluded.

“The plaintiffs here suggest that holistic review should be conducted without regard to race, but it is artificial to consider an applicant’s experiences and perspectives while turning a blind eye to race,” the universities said. “For many applicants their race has influenced, and will continue to influence, their experiences and perspectives.”

Others also backed Harvard. The American Council on Education, which represents college and university presidents nationwide, and 36 other higher-education groups told the court the lawsuit was “nothing more than the first step in a backdoor attempt” to undo Supreme Court precedent on affirmative action and end the consideration of race in college admissions.

A group called Asian Americans Advancing Justice joined with civil rights lawyers in a brief citing students who back Harvard’s policy, including Thang Diep, a Vietnamese American who is a senior at the university. “I support Harvard’s race-conscious admissions program and I do not think that Harvard discriminates against Asian Americans, but that does not mean that Harvard has done enough,” Diep said in a statement. He said Harvard needs more diversity among its Asian Americans.

But a group called the National Association of Scholars sided with the plaintiff, drawing comparison to limits Harvard and other elite schools put on Jewish applicants in earlier eras. “This record is replete with evidence of a de facto Asian quota startlingly similar to the one that Harvard once imposed on Jews; of impermissible racial proportionality, or ‘balancing,’ in admissions; and of biased views about the personal characteristics of Asian applicants,” the group wrote. Based in New York, the group opposes racial preferences in admissions. In 1996, it supported the anti-affirmative-action ballot initiative in California known as Proposition 209.

Harvard is one of the most selective schools in the country, with an admission rate below 5 percent. For the class entering this fall, it admitted 1,962 out of 42,749 applicants. Of those admitted, nearly 23 percent were Asian American and nearly 16 percent African American. Roughly 12 percent were Latino, and a little more than 2 percent were Native American or Native Hawaiian. Those figures include students who identified with more than one race or ethnicity. The rest of the admitted Class of 2022 were white students from the United States and international students from dozens of countries.