State Rep. Rich Brauer identifies the slain guard as 51-year-old William Wozniak, who was married with two teenage children. Wozniak was hit by a single gunshot in the chest and died in the operating room at the hospital as doctors tried to repair the damage.
Authorities have not said anything about a motive for the shooting, but WBBM-TV in Chicago reports on its web site that the gunman is said to have been upset over a dispute involving a gun permit.
The Illinois state Capitol building has no metal detectors and its officers are not armed.
Police say they believe the killer - who remains at large - was involved in both a shooting and attempted robbery about an hour earlier at a military surplus store just two miles away and in the theft of a shotgun from the same store a week before.
Col. Larry Schmidt, chief deputy director of the Secretary of State's police force, identifies the chief suspect in the killing as Derek W. Potts, 24, of Springfield. Police say Potts is named in an arrest warrant accusing him of murder, burglary and more.
Police have not found anyone who says they saw the shooting take place but several people have reported seeing the gunman leaving.
Officials are also reviewing footage from surveillance cameras in the area in the hopes of turning up a clue.
Acting on a tip, police searched Potts' apartment late Monday, but he was not home. Springfield Police Lt. Doug Williamson says police searching that address found both a stolen shotgun and a car in the parking lot similar to the getaway vehicle described by witnesses.
Police don't yet know if the gun is the same one that was used in the Capitol shooting.
Police have urged residents of the city of 112,000 to be cautious. Security was quickly tightened at nearby schools, and police said students near the Capitol who usually walk home alone were given escorts.
"There may be three criminal events linked to this one person. Right now, I can't think of any reason for this individual to stop committing criminal acts," Williamson said.
The shooter entered the north entrance and shot the guard at 1:38 p.m., said Randy Nehrt, a spokesman for the Secretary of State's Office. The shooting occurred just inside the building's entrance. The gunman used either a rifle or a shotgun.
"It just sounded like a bomb went off. Then someone immediately yelled, 'Someone's been shot,'" said Leslie Root, who works for a state senator on the first floor near the site of the shooting.
The Capitol was locked down for about an hour after the shooting, following an announcement over the intercom ordering everyone to stay in their offices.
Outside, police cars and ambulances surrounded the building, and officers roped off the entrance. After the lockdown was lifted, armed officers were in the halls and everyone entering the building was required to sign in, rather than the usual procedure of simply showing a badge.
Gov. Rod Blagojevich was not in the Capitol at the time, and the Legislature is not in session.
At a news conference Monday night, Blagojevich expressed his sympathy to the victim's family and called for tighter security, including metal detectors and possibly weapons for the security force.