The 19-year-old son of Presidential Counselor Edwin Meese was killed late Thursday night when his red Volkswagen veered off the northbound lane of the George Washington Parkway at high speed, traveled 330 feet and crashed into a tree.

Scott R. Meese, a sophomore at Princeton University and a summer intern with Senate Republicans, apparently was returning to his parents' home in McLean shortly before midnight when, police said, he lost control of the car and failed to negotiate a curve just south of the Rte. 123 exit.

Meese was trying to pass another car when his own car suddenly veered left and ran onto the grassy median strip. "He had to be going 85 -- extremely fast . . . When I saw him go by, I thought, 'God, that guy is going fast,' " said 20-year-old Anne Phillips of McLean, who said she was driving at about 60 mph. "I had never seen a car pass me that fast." The parkway has a 45 mph speed limit there.

Park police said that speed was probably the chief cause of the accident. "He was going at a high rate of speed, at least 75 to 80 miles per hour, probably faster than that, but I can't confirm it at this time," said Robert Stratton, a police spokesman. Police were still investigating late yesterday to determine whether alcohol or drugs were involved.

By the time police arrived, the engine of Meese's 1979 Volkswagen Dasher was on fire. Rescue workers, aided by an unidentified Air Force doctor, extracted Meese from the wreck but, according to police, it was too late. They said he showed no signs of life and was pronounced dead on arrival at Fairfax Hospital.

Police did not disclose the victim's name until 5 a.m. yesterday after the Secret Service reached his parents, both of whom were out of town. Edwin Meese, one of President Reagan's closest advisers, was in California for a meeting of the exclusive Bohemian Club; his wife, Ursula, was in Peru on a trip with longtime Reagan friend Nancy Reynolds, the U.S. representative to the U.N. Commission on the Status of Women.

Police said the elder Meese was informed of his son's fatal accident at 4:42 a.m., more than four hours after the crash. He arrived back in Washington yesterday afternoon. His wife was expected to return last night.

Upon hearing the news on Air Force One on his way back from St. Louis, President Reagan issued a statement of sympathy: "Nancy and I are shocked and deeply saddened. Our hearts go out to Ed and Ursula who, with their family, are close and dear friends of ours."

Scott Meese was working this summer for the Senate Majority Policy Committee where he was charged with organizing seminars for the estimated 300 summer interns working for Republicans on Capitol Hill. A recent speaker in the program was his father, who served as the president's chief of staff during Reagan's two terms as governor of California.

Last summer Scott Meese, the second of three children, worked for Sen. Paul Laxalt (R-Nev.), Reagan's top confidant in the Senate. Colleagues spoke highly of his good humor and talent. "Scott was a tremendous young man, bright and articulate, always smiling and with a great sense of humor," said Laxalt.

"He was the most cheerful person I knew in my life," said one of his supervisors, who asked not to be named, "He was a hard worker, probably the most willing worker we had. No job was too small for Scott."

In addition to his duties as an intern, Scott Meese was apparently an enthusiastic softball player, joining teams formed by the staffs of the policy committee, and the offices of Laxalt and Sen. John Tower (R-Tex.).

Ann Jones, press assistant to Tower, said that young Meese had spent yesterday evening with interns from her office. "He was with a bunch of our interns last night; I don't know where," she said.

The Meeses' other two children were also out of town this week. Michael, 21, a recent graduate of the U.S. Military Academy at West Point, was reported in Panama, and his sister, Dana, 15, in Alaska.