Washington — The suspect in the weekend shooting at the White House Correspondents' Dinner has agreed to remain detained in the lead-up to his trial.

During a hearing before U.S. Magistrate Judge Moxila Upadhyaya, a lawyer for the suspected gunman, Cole Allen, told the judge that he will not contest the government's effort to keep him in federal custody. 

Allen, 31, is charged with attempting to assassinate President Trump and two firearms-related offenses stemming from the shooting outside the annual press gala on Saturday. He made his initial appearance in federal court Monday. 

Allen has not yet entered a plea to the charges. A preliminary hearing is set for May 11.

Tezira Abe, a lawyer for Allen, told the court that he is being held in a "safe cell" under 24-hour lockdown, and she asked the judge to order the jail to lift those restrictions. The judge said while she would accept briefs on the matter, she did not have the authority to override the judgement of the jail.

Allen was escorted into the courtroom by three U.S. Marshals shortly after the hearing convened and was wearing a short-sleeve, orange jumpsuit. He has a goatee beard and short, curvy hair. Allen did not look at or address those in attendance.

Prosecutors had urged the court to order Allen detained pending a criminal trial, writing in a filing Wednesday that the crimes he is charged with are "among the most serious in the United States code, and the evidence of his guilt is overwhelming."

They said that Allen engaged in "extensive planning" for the attack and laid out a more detailed timeline of his movements and actions in the run-up to the dinner. Prosecutors also revealed in their filing a photo that they said Allen took of himself in the mirror of his hotel room, which showed him in a black dress shirt, black pants and what appears to be a red tie. 

In the image, Allen also appears to be armed with a sheathed knife, pliers, wire cutters and a small leather bag that looks like one filled with ammunition that was recovered from the scene, according to the filing.

Law enforcement officials said Allen, holding a shotgun, rushed a security checkpoint on the terrace level outside the dinner Saturday. Mr. Trump, Vice President JD Vance and many Cabinet officials were in attendance alongside scores of journalists, media executives and members of Congress. 

A U.S. Secret Service officer "observed the defendant fire the shotgun in the direction of the stairs leading down to the ballroom," prosecutors said in their memorandum, and the officer fired five times at the defendant. 

Allen fell to the ground, but was not hit by gunfire, and was apprehended by authorities, according to law enforcement. The Secret Service officer, identified as Officer V.G. in a FBI affidavit, was shot in his bulletproof vest and was not seriously injured, according to court papers. The filing did not say who fired the shot that hit the officer.

Senior law enforcement officials told CBS News on Wednesday that the round that struck the Secret Service officer was not friendly fire. Two sources familiar with the investigation said the shot that hit the officer likely struck a cellphone tucked into the pocket of the bulletproof vest.

Ahead of the hearing, Allen's lawyers had argued that he should be released ahead of a trial and told the court in a filing Wednesday that he has no criminal history and is college-educated. They said he was "gainfully employed" as a tutor, is a "devout Christian" who "dutifully" attends church and is an "active participant" in his religious community. Those factors, they said, weigh in favor of release.

But during the proceeding, Abe, Allen's lawyer, said that after meeting with him, he agreed to remain detained. 

In their filing, though, the defense lawyers had pushed back on the Justice Department's claim that Allen was willing to commit a "mass shooting" and said that assertion was not supported by the facts. Allen, they wrote, allegedly told family and friends in a letter sent just before the attack that he wanted to "minimize casualties" by using "buckshot."

"Moreover, the government after essentially asserting that Mr. Allen shot a Secret Service Officer in the criminal complaint, has apparently retreated from the theory by not mentioning the alleged officer at all in its memorandum," Allen's lawyers said of Officer V.G. "In sum, the government's entire argument about the nature and circumstances of the offense is based upon inferences drawn about Mr. Allen's intent that raise more questions than answers."

The defense attorneys further told the court that while Allen has been charged with attempting to kill Mr. Trump, the letter sent to his family and friends does not mention the president by name.

"The government's evidence of the charged offense — the attempted assassination of the president — is thus built entirely upon speculation, even under the most generous reading of its theory," they said. "While the government may be able to say that the letter expresses an intent to target administration officials, it falls well short of narrowing those officials to President Trump."

In a letter to Allen's lawyers Wednesday, prosecutors said that the investigation into the shooting is ongoing and an analysis of crime-scene evidence and ballistics evidence is not yet finished. They said that evidence shows that Allen fired his pump-action shotgun at least one time as he ran past the magnetometers outside the event Saturday night.

Ballistics and video analyses show that Allen fired his shotgun "in the direction" of the Secret Service officer, prosecutors wrote.

"The government is aware of no physical evidence, digital video evidence, or witness statements that are inconsistent with the theory that your client fired his shotgun in the direction of Officer V.G., or that Officer V.G. was indeed shot once in the chest while wearing a ballistic vest," they said.