At 1:30 p.m. yesterday as the military coordinators at 3d Street and Madison Drive NW waited for the first parade units to move out, the word came over the radio: the President was walking.

"He's walking, said an Army staff sergeant, astonished. He reached for the hotline telephone. The first bands would have to wait.

The military coordinators hadn't known. The civilian coordinators apparently hadn't known. The D.C. Police Department had expected him to walk part of the route, Chief Maurice J. Cullinane said, but not 30 minutes beforehand. A Secret Service spokesman said Carter told them three weeks ago.

Carter himself was fairly low-key about it. "We enjoyed the walk," he told reporters afterward."It's been something I've thought about for a long time . . . This was a good parade."

In addition to startling parade officials and delighting the crowds along Pennsylvania Avenue, Carter appears to have made history with his 16-block walk. A check at the National Archives yesterday indicated that while some Presidents have walked portions of the route and others have ridden it on horseback, none before Carter had ever walked the whole distance.

"I told the Secret Service about three weeks ago that I was going to walk all the way," Carter told reporters. "They said if we kept it quiet, they thought it would be all right, but if it got a lot of publicity it might not be good."

They kept it very quiet. Metropolitan Police, taken by surprise when the President and Mrs. Carter climbed out of their limousine in front of the Capitol and began to walk, quickly dispatched a few scooter policemen to recheck rooftops of buildings overlooking the parade route. Some spectators were cleared off the roofs, a police spokesman said, although no weapons were found.

"The security is pretty much the same whether he rode or walked." the spokesman said.

Secret Service spokesman John Warner said Carter told them three weeks ago that he might walk his route and that the service had accordingly prepared security as though the President were riding in an open rather that a closed, car. Agents were scattered in the crowds and placed on rooftops along the parade route, and Secret Service men nearly surrounded the Carters as they walked.

A woman in the crowd holding an empty champagne glass said, "Isn't Rosalynn brave? She hasn't even got a hat on."

Jasper Lewis, who lives in Washington, said admiringly, "Man, he got out and walked among the people like a man. Not like Nixon. He has got no reason to be scared."