Delaware State Police Sgt. Paul Shavack and Attorney General Beau Biden did not release the names of the shooter or any of victims, citing the continuing investigation and the need to notify family members.
Shavack said that police did not know how many bullets were fired or what kind of gun the shooter used. He also said authorities still were trying to determine whether the shooter was killed by police or took his own life.
Biden said at an afternoon news conference that the attack was not random, and that it was related to a custody battle that he described as long-standing. He declined to elaborate. The Wilmington News Journal identified one of the victims as Christine Belford, 39, who had been involved in a custody dispute with her husband.
Officials described the shooter only as a white man between 50 and 60 years old, and did not indicate whether the victim's husband might have been involved in the incident.
Police said the officers hit by gunfire were members of the Delaware Capitol Police, which protects state-owned facilities. They said one officer was a 50-year-old man who has served for less than a year; the other was a 42-year-old man who has served for seven years.
Shavack said the two were "doing well."
Authorities were searching the floors of the courthouse, on North King Street, throughout the day. Shavack said police did not believe the gunman had an accomplice.
The area surrounding the courthouse was blockaded by police cars in the hours after the incident. Many people waited outside the courthouse for loved ones to emerge.
One concerned onlooker was Marlene Bridgeforth, who got hold of her sister, a courthouse clerk, after trying to reach her by phone for about an hour. Her sister was fine but devastated by the shooting, Bridgeforth said.
"I couldn't get anything of what she was saying. She was gasping for breath," she said.
Harding, a parking attendant at the building, said that she took cover with about 100 others in the doughnut shop and that some were hiding in two small closets.
Robinson, a bailiff, said that she looked over the balcony above the lobby and heard gunshots before seeking cover in a nearby room.
"There was a lot of commotion," she said of the scene below, recalling broken glass and about 30 people in the area where shots were fired.
Brittany Mangrum said she was about to enter the courthouse to pay a fine when a group of people came running out from inside.
"I decided to turn and run with them," she said.
See a photo gallery and video from the scene of the shooting at the Wilmington courthouse at: www.philly.com/newcastle
Contact Chris Palmer, 609-217-8305, firstname.lastname@example.org, or follow on Twitter, @cs_palmer.
Philly.com staff writers Emily Babay and Frank Kummer contributed to this article.