The court’s 6-3 conservative majority is expected to be sympathetic in the eventual ruling, due by the end of June, toward the challenges to Harvard and UNC.

Conservative Justice Brett Kavanaugh told the lawyer defending UNC’s policy that “these racial classifications are potentially dangerous and must have a logical end point”.

“When is your sunset? When does this end?” conservative Justice Amy Coney Barrett asked about UNC’s consideration of race in admissions.

The universities have said they use race as only one factor in a host of individualised evaluations for admission without quotas – permissible under Supreme Court precedents – and that curbing the consideration of race would result in a significant drop in the number of students from under-represented groups.

Many institutions of higher education place a premium on achieving a diverse student population not simply to remedy racial inequity and exclusion in American life but to bring a range of perspectives onto campuses.

Conservative Justice Clarence Thomas, one of two black members of the court, said, “I’ve heard the word diversity quite a few times, and I don’t have a clue what it means.”

The court’s three liberal justices grilled Patrick Strawbridge, the lawyer for the challengers, in the UNC case.

“You keep saying that you object to the use of race standing alone” in deciding which applicants to admit, Justice Ketanji Brown Jackson, the first black woman to serve on the court, told Strawbridge.

“But as I read the record and understand their process, it’s never standing alone, that it’s in the context of all of the other factors – there are 40 factors about all sorts of things that the admissions office is looking at. And you haven’t demonstrated or shown one situation in which all they look at is race,” Jackson added.

The cases give the court an opportunity to overturn its prior rulings allowing race-conscious admissions policies.

They also give it a chance to embrace an interpretation favoured by conservatives of the US Constitution’s 14th Amendment promise of equal protection under the law that would bar governments and other institutions from using race-conscious policies – even those crafted to benefit people who have endured discrimination.

Liberal Justice Elena Kagan said, “I thought that part of what it meant to be an American and to believe in American pluralism is that, actually, our institutions are reflective of who we are as a people in all our variety.”

Conservative Chief Justice John Roberts said that if schools no longer are permitted to solicit applicants’ race through “checking a box” on an admissions application as they now can, “maybe there’d be an incentive for a university to, in fact, pursue race-neutral alternatives”.

Justice Sonia Sotomayor, the only Hispanic person ever to serve on the court, pointed to disadvantages that black applicants might have experienced before applying to attend a college.

“If you’re black, you’re more likely to be in an under-resourced school, you’re more likely to be taught by teachers who are not as qualified as others, you’re more likely to be viewed as having less academic potential,” Sotomayor said.

Blum’s group said UNC discriminates against white and Asian-American applicants and Harvard discriminates against Asian-American applicants.

The suits were filed separately against the two schools in 2014. One accused Harvard of violating Title VI of the Civil Rights Act of 1964, which bars discrimination based on race, colour or national origin under any programme or activity receiving federal financial aid. The other accused UNC violating the 14th Amendment.

Blum’s group has argued that the Constitution requires colourblind admissions.

“The assumption that race necessarily informs something about anyone’s qualifications is antithetical to this court’s precedents and to our Constitution,” Strawbridge told the justices.

Conservative Justice Samuel Alito asked whether if schools are barred from considering race they could still consider, in the theoretical case of an immigrant from Africa now living in a predominately white area in North Carolina, an essay that describes having to deal with “huge cultural differences”.

Strawbridge said such an applicant could do so “because the preference in that case is not being based upon the race”.

Kagan pushed back on that scenario, saying it was “slicing the baloney awfully thin” because “race is part of the culture”.

The two schools and President Joe Biden’s administration, backing them, said categorically banning any consideration of an individual’s race would be inconsistent with equal protection.

Demonstrators gathered outside the court building ahead of the arguments.

Affirmative action has withstood Supreme Court scrutiny for decades, including in a 2016 ruling involving a white student, backed by Blum, who challenged the University of Texas after being rejected for admission, though the justices have narrowed its application. The Supreme Court has shifted rightward since 2016.

Blum’s group asked the Supreme Court to overturn a 2003 Supreme Court ruling in a case called Grutter vs Bollinger involving the University of Michigan Law School that held that colleges could consider race as one factor in the admissions process because of the compelling interest of creating a diverse student body.

The Supreme Court first upheld affirmative action in college admissions in a 1978 ruling in a case called Regents of the University of California vs Bakke that held that actions to achieve diversity were permissible but racial quotas were not.