(CNN) — Five people remain hospitalized Friday, a day after a man walked into a Pittsburgh psychiatric hospital with a pair of guns and started shooting.

Michael Schaab, 25, died after being shot by the gunman, and the gunman himself was killed by police, authorities said. Schaab was an employee at the University of Pittsburgh Medical Center’s Western Psychiatric Institute and Clinic, where the incident took place.

Two of the seven people wounded have been released from the medical center, according to hospital spokeswoman Wendy Zellner.

Those who remained hospitalized are all employees of the psychiatric center. They include a 46-year-old man listed in fair condition; a 64-year-old woman in serious condition; a 54-year-old woman in good condition; a 35-year-old man in fair condition; and a 49-year-old man in serious condition, authorities said.

“This is a tragic day, a sad day, a senseless day,” Mayor Luke Ravenstahl said after the shooting Thursday at the medical center.

City and hospital officials speaking at a Thursday evening press conference did not give the identity of the shooter, nor did they elaborate on what his motive might have been.

The assailant walked through the psychiatric hospital’s front door with a pair of semi-automatic handguns around 1:40 p.m., according to Ravenstahl.

Officers from the University of Pittsburgh police department arrived within “a matter of minutes” and “engaged” the gunman, the mayor added.

“There is no doubt that their swift response saved lives today,” said Ravenstahl, lauding the police officers’ “courage and willingness to step up.”

Those wounded were swiftly ushered to nearby UPMC Presbyterian. All are expected to survive.

Officials said two of the five hospitalized patients have undergone surgery.

Ravenstahl said that a University of Pittsburgh police officer “was grazed with a bullet, and I believe he is doing well.”

Steven Bartholomew, a spokesman for the federal Bureau of Alcohol, Tobacco, Firearms and Explosives, said his agency is “working with Pittsburgh police and other authorities in the investigation.”

“Any firearms recovered will be traced to determine their source,” Bartholomew said.

At one point Thursday, the University of Pittsburgh’s official Twitter account had a message that suggested a “possible 2nd actor” was involved and called for a lockdown.

But later in the day, the medical center’s Twitter feed had a message insisting “there was no second shooter” and there was “no hostage situation,” as had been reported elsewhere.

The psychiatric hospital’s CEO, Claudia Roth, emphasized after the shooting that treatment at the facility “will be uncompromised,” with care continuing to be delivered through the day and night “the same way we always have.”

— CNN’s Jeremy Ryan contributed to this report