The U.S. attorney's office asked the full bench of the U. S. Court of Appeals here yesterday to overturn an earlier ruling that bars use of certain evidence in the government's case against John W. Hinckley Jr., who attempted to assassinate President Reagan last year.

The government's action had been widely anticipated since the U.S. solicitor general approved the appeal on March 12. It could delay the start of Hinckley's trial for several months if the full court agrees to hear the case.

The prosecution wants to use statements Hinckley made to federal agents shortly after his arrest, as well as some documents seized from his prison cell, to show that he was not insane when he shot Reagan, the president's press secretary, a Secret Service agent and a D.C. police officer.

Last November, U.S. District Judge Barrington D. Parker ruled that FBI agents had violated Hinckley's rights by continuing to question him after he had asked for a lawyer. Parker said Hinckley's statements to the agents could not be used, nor could certain items seized from his cell in Butner, N.C.

A three-judge appellate panel agreed with Parker, and the government then elected to petition the full bench of the appeals court.