Richard E. Burke, the top aide to Sen. Edward M. Kennedy (D-Mass.) and a man who last month complained to District of Columbia police that he was the victim of numerous death threats, a shooting and a break-in, admitted yesterday that the incidents were a hoax.

Burke abruptly resigned from Kennedy's staff and in a brief and hastily written letter told Kennedy that "due to accumulated stress from the campaign, and reorganization of the office, events that happened to me in early February were of my own creation. I have voluntarily revealed the truth to the proper authorities. I have sought comprehensive medical advice and am currently receiving the recommended treatment."

Meanwhile, the U.S. Attorney's office here is considering whether to bring charges against Burke for providing false information to law enforcement officials and discharging a firearm in the District D.C. police, the FBI and the Secret Service spent several weeks investigating the alleged death threats.

Burke told investigators last month that he had been the subject of numerous recent death threats. At one point, he said an intruder had broken into his home at 3 a.m. and had stuck a butcher knife in his locked bedroom door before fleeing when his burglar alarm went off. Two days later, on Feb. 9, Burke told police he had been shot at while he sat in his car in the driveway of his fashionable Northwest Washington Home. A bullet had crashed through the windshield of the car.

In all, Burke told investigators that he had received death threats in a letter, two notes and seven telephone calls. The FBI became involved when one of the notes, purportedly received at Kennedy's office, seemed to suggest an extortion attempt. The Secret Service joined the task force of investigators when one of the notes -- purportedly hurled against Burke's house wrapped in a pipe -- contained a threat against President Reagan's son, Ron.

"It's absurd. It's like a bad dream. It's very scary," Burke told a Washington Post reporter on Feb. 13. He hired a private security firm to provide round-the-clock protection and seemed frightened to his friends, but continued to go to work while investigators tried to determine who was after him.

Burke went on a leave of absence March 1, and his colleagues seemed not to know that he had made up the incidents himself until a Washington Post reporter called yesterday afternoon to ask if it were true. After conferences that lasted for several hours, Bob Shrum, Kennedy's press aide, said that Burke was submitting a letter of resignation to the senator, and that the staff would be informed at the close of the day.

Kennedy issued the following statement late yesterday: "I have accepted Rick Burke's resignation with regret and with deep gratitude for his extraordinary service as my administrative assistant. I value his friendship; he has my total support during this difficult period."

Burke, a 27-year old bachelor, joined Kennedy's staff as a teen-ager and worked himself up the staff ladder from a clerk to become the senator's closest aide. He won his position through single-minded dedication and loyalty to the senator, according to friends. He worked long hours, was willing to undertake any task for Kennedy and at times volunteered to baby-sit for his children.

At the end of his resignation letter to Kennedy, Burke said that he was "grateful for the support of my family, friends, and especially you during these difficult times." Shrum said that Burke did not want to be interviewed and that there would be no further statements on the matter from Kennedy's office.

Law enforcement sources said yesterday that D.C. police, FBI and Secret Service had referred reports on the case to the grand jury section of the U.S. Attorney's office, and that a decision is expected to be made within two weeks whether to prosecute Burke.