Students for Fair Admissions, fresh off its Supreme Court victory gutting affirmative action in college admissions, is preparing for another potential lawsuit.

The group is soliciting possible plaintiffs — applicants rejected from the U.S. Military Academy, known as West Point; the Naval Academy; and the Air Force Academy — for an effort to challenge race-conscious admissions at the three major American service academies, which are responsible for educating and training many of the country’s future military leaders.

“Were you rejected from West Point?” asks a new webpage, WestPointNotFair.org, set up on Thursday and apparently aimed at white and Asian applicants. “It may be because you’re the wrong race.” It goes on to urge, “Tell us your story,” and provides a form requesting detailed contact information.

Affirmative action at U.S. military academies was not addressed by the Supreme Court ruling in June, because Chief Justice John Roberts wrote, in a footnote, that they had “potentially distinct interests.”

The federal government argued in its brief to the court that race-conscious admissions in the military was needed to create a pipeline of Black and Hispanic officers, and maintain morale among the troops. Racial integration in the military is a matter of national security, the government said.

“The nation’s military leaders, for example, have learned through hard experience that the effectiveness of our military depends on a diverse officer corps that is ready to lead an increasingly diverse fighting force,” the government said.

Students for Fair Admissions said in a statement that “the culture of the armed services requires that each warfighter see fellow warfighters as totally committed teammates, where race, ethnicity and heritage, while respected, do not matter.” Opponents of racial preferences in the service academies argued that they worked against efforts to defend the country.

“The military’s use of racial preferences today is unquestionably harmful to our national security,” said Veterans for Fairness and Merit, representing more than 600 former members of all branches of the U.S. military, in a brief supporting Students for Fair Admissions in the Supreme Court case.

In response to the Students for Fair Admissions criticism, the Defense Department said that it was still evaluating the implications of the court’s affirmative action decision. “We rely on a pipeline of highly qualified American patriots from all walks of life and all backgrounds, which is crucial for our national security,” it said in a statement.

The U.S. armed forces rely on a race-conscious admissions system both in admitting students to the military academies and in recruiting officers from civilian universities like Harvard, according to the government brief.

In 1968, there were 30 African American cadets at West Point; by 1971, there were almost 100, according to court papers.

West Point’s incoming class of 2027 includes 127 African Americans, 137 Hispanic Americans, 170 Asian Americans and 18 Native Americans, out of a class of about 1,240.

The service academies are highly selective, with incoming classes winnowed from a pool of 10,000 or more applicants, according to federal data. Applicants are required to meet academic and fitness requirements and be nominated, typically by a member of Congress. Tuition is free, but, in return, graduates have to serve in the military.

The question of how to handle racial preferences in the military has come up before, notably in Grutter v. Bollinger, a 2003 case in which the Supreme Court upheld the University of Michigan Law School’s use of race in admissions.

In that case, high-ranking officers and civilian leaders of the military argued in an amicus brief that the military could not achieve an officer corps that was highly qualified and racially diverse without using limited race-conscious recruiting and admissions policies in both the service academies and R.O.T.C.

The brief in the 2003 case cited the Vietnam War era as an illustration of the dangers of having too few minority officers in the military. At the end of the war, the brief said, only 3 percent of Army officers were Black.

“The danger this created was not theoretical,” it said. “As that war continued, the armed forces suffered increased racial polarization, pervasive disciplinary problems and racially motivated incidents in Vietnam and on posts around the world.”