Three victims, one of them a 16-year-old youth, were in critical condition and one serious, a hospital spokesmen said.
Man in trench coat
Witnesses told local media that the shooting began when a man wearing a trench coat and carrying a backpack fired at random with a pump-action shotgun.
Barrett Dodds, an antique shop owner, said he saw a man in a rain coat exchanging gunfire with a police officer before the armed man was cornered in a children's clothing shop.
"I saw the cops go in the store. I saw the shooter go down," said Dodds, who watched from the second floor.
A witness who was in another antiques shop when two women in a frantic state ran in and reported the firing.
"We heard shot after shot after shot - loud, loud, loud," said Barb McKeown. She hid under a staircase with three other people until it the shooting stopped.
The two-storey building shopping mall, southeast of Salt Lake City's business centre, is a refurbished trolley barn, with a series of winding hallways and about 80 shops.
In the second shooting incident, according to CBS news, a lone armed man opened fire on at least four people before turning the gun on himself late on Monday.
At least three of those shot were killed, while a fourth was admitted to hospital.
The motive for the shooting was not immediately known.
Police in Philadelphia, Pennsylvania, were not immediately available to confirm the report.
According to KYWTV station, a local TV station in Philadelphia, one victim survived the shooting and was rushed to hospital.
The incident occurred at an office complex that housed an internet marketing company, CNN reported, quoting a police source.