Presidential assailant John W. Hinckley Jr., speaking in a steady voice, told a federal judge at a hearing in U.S. District Court here yesterday that "I now cherish my life" and asked for a chance to prove "to the entire world that I am getting well."

Dressed in a tan, three-piece suit, Hinckley stood at the lectern and read a five-minute statement in which he asked for broader privileges during his confinement at St. Elizabeths Hospital. "I'm not the same person I was two years ago," Hinckley said. "I no longer need protection from myself."

Judge Barrington D. Parker denied Hinckley's request for more telephone and grounds privileges and access to the press, saying he was acting on the recommendation of Hinckley's psychiatrist.

Hinckley, 29, has been held at the hospital since June 1982, when he was found innocent by reason of insanity in the March 1981 shooting of President Reagan and three other men.

Under District law, Hinckley is entitled to request his release from St. Elizabeths at six-month intervals. He has never done so. Yesterday's hearing was limited to the request for looser restrictions, which was opposed by federal prosecutors.

Hinckley's courtroom demeanor was in marked contrast to his conduct during his trial two years ago, when he behaved erratically. He was accompanied by the two attorneys, Vincent Fuller and Judith Miller, who defended him at his trial.

Parker permitted Hinckley to speak on his own behalf but he was not allowed to cross-examine hospital officials.

Dr. Joan A. Turkus, Hinckley's psychiatrist, testified that censorship of Hinckley's mail was stopped this week because of improvement in his condition. She said doctors favor lifting restrictions on Hinckley's telephone use in the near future if he proves he can handle his new freedom with his mail.

In his statement to Parker, Hinckley said fears that he would use media interviews to speak out about actress Jodie Foster -- whom he fantasized about impressing by shooting Reagan, according to trial testimony -- were unfounded. "My obsession with Jodie Foster has been over for 19 months," he said.

Hinckley told Judge Parker, who presided at his trial, that he had been told by hospital officials that he was "clinically ready" to walk the grounds of St. Elizabeths for an hour a day, accompanied by a staff member.

"What I actually said to Mr. Hinckley on several occasions," said Turkus, "was that he had some clinical readiness. It is not total. There are still some clinical and security issues to be worked through."

Hinckley said he would be willing "to wear a bulletproof vest and walk with an armed guard" if allowed occasionally to leave the confines of the hospital's John Howard Pavilion, which he described as "suffocating."

"I have become so discriminating that I would grant interviews to very few," Hinckley said. "I have never tried to profit financially from the tragedy of March 31, 1981. I seek self-respect and dignity from interviews, not financial gain."

Hinckley appeared nervous at the start of the hour-long hearing in Parker's heavily guarded courtroom, exhaling deeply several times as if to calm himself. He removed a clip-on necktie after about 10 minutes and handed it to a U.S. marshal.

At the lectern, his voice was steady. He reacted calmly when interrupted twice by Parker. "When I came to St. Elizabeths on June 22, 1982, I did have mental problems," Hinckley said. "I was out of control two years ago and restrictions were necessary . . . . I did some very stupid, very sick things."

He said he believed the restrictions now are "unfair and totally unnecessary." Hinckley said he wanted freer use of the telephone, in part because "my parents will soon be living in the D.C. area and I'll be calling them daily."

Hinckley's parents, who live in Evergreen, Colo., near Denver, founded the American Mental Health Fund in Falls Church about a year ago to help raise funds for research on mental illness. A fund employe said the Hinckleys plan to move here by the end of the year to devote full time to the organization and to be near their son.

Hinckley called restrictions on his access to the media "very unfair and perhaps unconstitutional." Hospital officials have said that maximum security patients, including Hinckley, are not allowed to speak to the press.

Hinckley contended yesterday that the policy is aimed specifically at him. "I am, of course, the most well-known patient at St. Elizabeths," he said, "and the only one the media cares about."

Hinckley said he had spent 13 months "in a very depressed state, waiting for trial" and that his first six months at St. Elizabeths after trial were "bleak. I was still obsessed, depressed and desperate." At one point, he said, "I attempted suicide, and thank God I failed.

"I now cherish my life. I never again want to harm another human being. I am ready for some responsibility. Please give me an opportunity to prove to you, the hospital and the entire world that I am getting well."