Government prosecutors yesterday lost their bid to have the full U.S. Court of Appeals review a judge's ruling that blocked the use of some evidence against John W. Hinckley Jr.

As a result, prosecutors said they will ask the court immediately to set a date for Hinckley's long-delayed trial on charges that he attempted to assassinate President Reagan outside the Washington Hilton Hotel more than a year ago.

The Justice Department, in a statement released just hours after the appeals court decision, said it continues to believe that Judge Barrington D. Parker's ruling that the statements and documents could not be used because they were illegally seized from Hinckley "presents important issues that have not been correctly resolved."

Nevertheless, the department said, the prosecutors would not ask the U.S. Supreme Court to review the question--a move that would be certain to further delay Hinckley's trial. "We have concluded that the broader interests of justice require that there be no further delay in the trial of this case," the department's statement said.

The Justice Department decision came shortly after the full U.S. Court of Appeals declined, 7 to 4, to review Parker's decision, which had been upheld earlier by a three-judge appeals panel.

In February, the three judge appeals panel upheld Parker's ruling that FBI agents had violated constitutional safeguards against self-incrimination when they continued to interview Hinckley after his arrest last March 30 despite his repeated requests to talk to a lawyer.

Moreover, Parker said--and the appeals panel agreed--prison guards at Butner, N.C., also violated Hinckley's constitutional rights to privacy when they seized documents from his cell at the institution, where he was confined for psychiatric examinations.

In March, the prosecutors asked the full 11-member appeals court to review the panel's decision, which they felt would prohibit them from using evidence to counter Hinckley's claim that he was insane at the time of the shooting and thus should not be held criminally responsible for his actions.

Hinckley's lawyers have conceded that he fired the shots that struck Reagan and three others. His trial is expected to focus on the question of whether he was sane when he committed the acts.

It was unclear yesterday when Hinckley's trial would be scheduled to begin. Several pretrial issues remain to be resolved, including whether the government should have to prove to a jury that Hinckley was sane when he committed the criminal acts or whether his lawyers should have to prove he was insane at the time.

Hinckley, 26, is currently being held at the army stockade at Fort Meade, Md.