In an interview with the military writer Thomas P. M. Barnett last year, Mr. Rumsfeld said, “I play squash with him,” gesturing at Mr. Di Rita. “When I pass him in a shot and it’s a well-played hard shot, I saw speed kills. And it does. If you can do something very fast you can get your job done and save a lot of lives.”

Many politicians have relaxed by competing, and Mr. Rumsfeld is not the first to have earned a reputation for zeal. As governor of New York, Mario M. Cuomo was known for his sharp elbows and tongue on the basketball court; as president, Bill Clinton exasperated his golf partners by taking mulligans, or do-overs, after bad shots.

In squash, Mr. Rumsfeld’s main advantage over more capable and fitter players is that he refuses to play anything but “hardball,” a variation of the game that was once common in the United States but has largely died out over the last decade. Most competitors now play the international game, which uses a softer ball and a wider court, requiring more running and allowing more creative shot-making. The harder ball favored by Mr. Rumsfeld tends to come back to the center of the court, so players do not have to move as much to return it.

The Pentagon gym had eight hardball courts when it was built in the 1940’s. When a new facility was built in 2002, one hardball court was kept for Mr. Rumsfeld and the handful of other Pentagon employees who still play that version of the game.

But some who know him say Mr. Rumsfeld refuses to concede that the game may have passed him by.

“One time I saw Rumsfeld and I referred to hardball as an old man’s game, and he just stared at me,” says David Bass, a public relations executive who sometimes plays on the Pentagon courts. “It’s become a running joke with us.”

Nor does Mr. Rumsfeld lack for bravado. Mohamed Awad, a former champion player who was once ranked as high as ninth in the world, spent a half hour hitting with him last February at a racquet club in Munich, where Mr. Rumsfeld was attending a military conference.

Mr. Rumsfeld plays well for a man his age, Mr. Awad said. Afterward, he said, Mr. Rumsfeld suggested that he could outplay another septuagenarian politician still known for his prowess in squash, the 78-year-old Egyptian president, Hosni Mubarak.