Exhausted and in apparent distress, President Carter dropped out slightly past the midpoint of a 6.2-mile race in the hills near Camp David, Md., yesterday.

A few hours later, he joined other runners at a picnic and said, "I feel great."

White House spokesmen, obviously seeking to minimize what some Carter aides thought could be a politically embarrassing incident, said no medical tests were given and "there is no reason for concern."

But there were moments of anxiety earlier, when Carter, wobbly and moaning, was kept from collapsing by security men who held him erect as he staggered to the top of a long hill in the fourth mile of the Catoctin Mountains race.

Colman McCarthy, a Washington Post reporter who was running in pace with Carter, described the president as "ashen" and in distress.

Carter was assisted to a golf cart, where the White House physician, Dr. William Lukash, examined him and urged the president not to run any farther. He moved to a White House car and was driven into Camp David to recover.

The incident occurred just 200 yards past the entrance to Camp David as Carter neared the top of the second major hill on the course. Between 800 and 900 runners were participating in the event.

Lt. Col. Paul Kramer of Washington, who was jogging close behind Carter, told United Press International he saw "his legs collapse. He looked in pretty bad shape. His head was down, and he just looked lousy."

The cause of Carter's extreme fatigue was not evident to fellow runners. The weather was cool, and the race was not considered challenging for a runner in training.

Carter later told guests at the runners' picnic that he got in trouble by trying to better his previous record for the course.

"Our best time was 50 minutes, and we were trying to cut that by about four minutes today and didn't quite make it," the Associated Press quoted him as saying.

"They had to drag me off," Carter said. "I didn't want to stop." He said he remained "an evangelist" for running.

The White House did its best to minimize the incident. Annette Samuels, the duty officer in the press office, told inquirers, "It's merely a question of his being tired." She noted that Maj. Robert Peterson, Carter's military aide, "dropped out about the two-mile mark, and he's 20 years younger." Carter who was a cross-country runner at the Naval Academy, began jogging at the White House in the autumn of 1978 and regularly runs from three to seven miles at a clip. He jogged for 30 minutes or more several times during his vacation on the Mississippi riverboat Delta Queen and told reporters earlier this summer that he was pleased that the exercise had reduced both his weight and his pulse rate.

The incident was the latest public embarrassment to befall the politically beleaguered president, and triggered first a wave of personal concern and then of political nervousness among his aides.

"I suppose this will replace the rabbit stories," said one White House lieutenant, referring to the jokes that followed the recent disclosure of Carter's encounter with a seemingly malevolent swamp rabbit at his Georgia farm.

Another aide asked: "Are you going to headline it, 'Carter Drops Out of Race'?" Associates have been insisting all week that Carter would not drop out of a contest for the Democratic nomination with Sen. Edward M. Kennedy (D-Mass.).