The bystander who was struck when Secret Service agents exchanged fire with a gunman near the White House grounds was in stable condition on Sunday, according to law enforcement officials, as the police in Washington continue to investigate the attack.

The gunman, Nasire Best, 21, of Dundalk, Md., approached the northwestern corner of the White House complex a little after 6 p.m. on Saturday, officials said.

Mr. Best took a gun from his bag and began shooting toward a Secret Service checkpoint, according to a statement from the Metropolitan Police Department. Secret Service agents returned fire, killing him.

An adult male bystander, who has not been publicly identified by law enforcement, was struck amid the hail of gunfire and was taken by emergency medical workers to a hospital. He underwent surgery and was in stable condition, according to the Secret Service and Metropolitan Police.

The police are investigating to determine who shot the bystander.

Investigators will also piece together a more complete picture of the shooting, including how many shots were fired and whether the Secret Service was justified in its use of force.

Once the investigation is complete, the U.S. Attorney’s Office for the District of Columbia will independently review the facts and evidence in the case.

No Secret Service agents were harmed, according to the agency.

Television reporters were taping news segments on the north lawn of the White House before the attack, and their audio captured what sounded like dozens of shots fired by Mr. Best and the Secret Service.

Mr. Best had been on law enforcement’s radar for nearly a year.

Secret Service had flagged him “for walking around the White House complex inquiring how to gain access at various entry posts,” according to an affidavit filed in D.C. Superior Court.

In June, Mr. Best blocked a vehicle from entering the east side of the White House, the affidavit said, and he was arrested on a misdemeanor charge of unlawful entry. He told officers that “he was Jesus Christ and that he wanted to get arrested,” according to the affidavit.

In July, he entered a restricted area of the White House grounds after ignoring signs and commands to stop. After his arrest, a judge scheduled an August hearing and issued a “stay away order” to keep him from the area around the White House.

When Mr. Best did not show up to the hearing, the judge issued a bench warrant, authorizing his arrest.

Mr. Best lived just outside of Baltimore, Md., but the warrant only allowed officers to arrest him within the District of Columbia. It is not clear whether Mr. Best entered the district between August and the shooting on Saturday.