ARLINGTON, Va. — The solemn ritual of a burial with military honors is repeated dozens of times a day, in foul weather or fair, at Arlington National Cemetery, honoring service members from privates to presidents. But in order to preserve the tradition of burial at the nation’s foremost military cemetery for future generations, the Army, which runs Arlington, says it may have to deny it to nearly all veterans who are living today.

Arlington is running out of room. Already the final resting place for more than 420,000 veterans and their relatives, the cemetery has been adding about 7,000 each year. At that rate, even if the last rinds of open ground around its edges are put to use, the cemetery will be completely full in about 25 years.

“We’re literally up against a wall,” a spokeswoman for the cemetery, Barbara Lewandrowski, said as she stood in the soggy grass where marble markers march up to the stone wall separating the grounds from a six-lane highway. Even that wall has been put to use, stacked three high with niches for cremated remains.

The Army wants to keep Arlington going for at least another 150 years, but with no room to grow — the grounds are hemmed in by highways and development — the only way to do so is to significantly tighten the rules for who can be buried there. That has prompted a difficult debate over what Arlington means to the nation and how to balance egalitarian ideals against the site’s physical limits.

The strictest proposal the Army is considering would allow burials only for service members killed in action or awarded the military’s highest decoration for heroism, the Medal of Honor. Under those restrictions, Arlington would probably conduct fewer burials in a year than it does now in a week.

A policy like that would exclude thousands of currently eligible combat veterans and career officers who risked their lives in the service and who planned to be buried in Arlington among their fallen comrades.

“I don’t know if it’s fair to go back on a promise to an entire population of veterans,” said John Towles, a legislative deputy director for Veterans of Foreign Wars who deployed to Iraq and Afghanistan. The group, with 1.7 million veterans, has adamantly opposed the new restrictions.

“Let Arlington fill up with people who have served their country,” said Towles, who is eligible under current rules because he was wounded in battle. “We can create a new cemetery that, in time, will be just as special.”

There are 135 national cemeteries maintained by the Department of Veterans Affairs across the country. But Arlington is by far the most prominent, and curtailing burial there would mean changing the site from an active cemetery into something closer to a museum.

The Army is conducting a survey of public opinion on the question through the summer, and expects to make formal recommendations in the fall.

“What does the nation want us to do?” Arlington’s executive director, Karen Durham-Aguilera, said in an interview. “If the nation has the will to say we want to keep Arlington special and available, we have to make a change.” In a fitting turn of history, the cemetery now faced with a threat of overcrowding was created to address overcrowding. Early in the Civil War, the heavy death toll in battles near the capital soon filled Washington’s existing cemeteries. Desperate for more burial space, the Quartermaster General of the Army, Montgomery C. Meigs, turned to a rolling green plantation just across the Potomac — the home of Gen. Robert E. Lee, whose decision to fight on the Confederate side marked him as a traitor in many Union eyes.

Meigs’ men began burying corpses beneath simple wood markers in the fields, and then, in a grim rebuke to the absent owner, lined the flower garden with the graves of Union officers and built a tomb near the door of the plantation house to hold the bones of 2,100 unknown dead.

At first, Arlington was anything but a coveted resting place. Most early burials were of soldiers whose families could not afford to have their remains shipped home. But as revered Union officers chose to be buried in Arlington among the troops, the cemetery rose in prestige. The Tomb of the Unknowns was erected after World War I, and on nearly every Memorial Day since, the sitting president has laid a wreath there.

Among the limestone rows are milestones of human progress: The first explorer to map the Grand Canyon, the first person killed in an airplane crash, the first astronauts to die trying to reach space. Some distinguished themselves on the battlefield, others in later life, including Albert Sabin, who served briefly as a wartime Army doctor and went on to develop a polio vaccine, and Oliver Wendell Holmes Jr., a wounded Civil War lieutenant of little distinction who later became a Supreme Court justice. Most would have been barred under restrictions now being contemplated by the Army.

The modern concept of Arlington — an egalitarian Elysian field where generals and GIs of every creed and color are buried side by side — did not truly emerge until the cemetery was desegregated after World War II, according to Micki McElya, a history professor at the University of Connecticut.

“Many look to the place as a self-evident case for national inclusion and belonging, as an expression of the many and diverse become one,” McElya said in an interview. That, she said, is the Arlington cited by Khizr Khan, the father of an Army captain killed in Iraq and buried at the cemetery, when he urged Donald Trump to visit.

“Look at the graves of brave patriots who died defending the United States of America,” Khan said in his speech at the 2016 Democratic National Convention. “You will see all faiths, genders, and ethnicities.”

Now, though, that all-inclusive idea is bumping up against the lack of space.

Arlington has tried to stretch what room it has. It ended the old practice of burying family members side by side, and now stacks them two or three deep in a single plot. In sections that hold only cremated remains, the rows are now spaced closer together. But planners say those measures can do only so much.

Under current rules, burial plots in Arlington are open to veterans who served long enough to retire from the military; to troops who were wounded in battle or received one of the three highest awards for valor; to prisoners of war; to troops who die while on active duty; and to a few civilians who serve in high-level government posts. Their spouses and dependents are also eligible.

The Army has laid out several proposals for changing those rules to keep Arlington open longer, but only the most restrictive options would make much difference — and those are the least popular among veterans.

“Everybody wants to see Arlington stay open,” said Gerardo Avila, a wounded Iraq veteran who spoke to Congress on the issue on behalf of the American Legion. He said that while he would gladly give up his own spot to ensure a place for a future Medal of Honor recipient, the Legion, with 2.3 million members, does not share that view.

“You are voting your own rights away,” he said. “I’m not sure our members are willing to do that.” Army surveys indicate that the public supports giving priority to troops killed in battle or awarded the Medal of Honor. But it is not hard to find graves in Arlington of arguably deserving men and women who did neither.

On a recent evening, Nadine McLachlan knelt before the grave of her husband, Col. Joseph McLachlan, to trim the grass with scissors before arranging a bright vase of lilies. McLachlan was a fighter pilot who strafed the beaches of Normandy on D-Day; a week after, he was shot down and, though wounded, made his way back through enemy lines to safety. He went on to fly more than 100 more missions, earning the Legion of Merit, the Distinguished Flying Cross and 17 Air Medals for acts of heroism in flight.

He survived the war and lived for six more decades, until 2005. So under the most restrictive proposals, he would not qualify for burial at Arlington.

“My Joe was a wonderful man — very courageous, very kind,” Nadine McLachlan said. “I’m not sure that’s fair, to cut out men like him. They were in the line of fire, even if they made it. Being buried here with his friends meant a lot to him. It really is a dilemma.”