A friend of alleged cop killer Darrell Fuller told detectives the defendant admitted to him that he shot a police officer, according to a prosecution court filing.

Prosecutors say in the recent filing that Gerald Williams also told police he saw Fuller with a gun and was part of a scheme to try to conceal Fuller's involvement in the slayings of Nassau County police Officer Arthur Lopez and motorist Raymond Facey.

Authorities previously have said Fuller, 34, of St. Albans, "staged his own shooting" to make himself look like an innocent victim after gunning down both men on Oct. 23, 2012.

Fuller has pleaded not guilty and is facing life in prison without parole if a jury finds him guilty of first-degree murder at his upcoming trial.

Authorities say Fuller shot Lopez during a traffic stop near the Nassau-Queens border after fleeing an accident scene, before escaping the area by shooting and carjacking Facey, 58, of Brooklyn, on the Cross Island Parkway.

Nassau County Judge Jerald Carter has ordered juror pre-screenings to start April 28, but Fuller's attorneys are trying to suppress some of the government's evidence.

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Williams, 27, is jailed on weapons charges linked to the case after authorities previously said they found the gun used in the slayings, and a second gun, in the trunk of a car Williams let Fuller use that day.

Carter signed an order last month allowing Nassau investigators to release Williams from jail for part of one day after they said he had information relevant to the Fuller investigation.

The government's request for Williams' temporary release said Fuller called Williams and asked to meet him on Francis Lewis Boulevard on the day of the shootings. It said Williams told police he saw Fuller with a Ruger 9-mm semiautomatic gun, and Fuller told him he'd shot a police officer.

The filing also says Williams, along with two other people, tried to help Fuller cover up his crimes by making it look like Fuller "was the victim of a robbery, abduction, and shooting."

Eyewitness identifications and Fuller's alleged statements to police are among evidence his attorney, Kenneth St. Bernard, wants thrown out.

St. Bernard didn't return messages seeking comment, but said in court papers filed recently that a "tsunami of police generated prejudicial media publicity" prejudiced witness identifications of Fuller.

He said Fuller's mug shot, as released by law enforcement officials, was broadcast on television more than 24 hours before the first live police lineup.

The attorney also argued that Fuller's statements should be suppressed because authorities had him in custody for about 40 hours before arraignment, an abuse of the defendant's rights to counsel and to be arraigned without delay.

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The Nassau district attorney's office declined to comment on recent court filings, but argued in court records that police didn't have to give Fuller a Miranda warning before asking his name or who shot him.

They also argued that police gave Miranda warnings -- and Fuller waived rights -- before police kept questioning him, and that there was "no impropriety" tainting lineup procedures.