Bass said that it was not known whether the shooting was a targeted attack but there did not appear to be a larger threat to the public.
Bass says no other victims or suspects were found inside the mall. The man is in critical condition and the woman in serious condition.
Two people in their early 20s were shot at about 1.30pm (local time) near the southeast entrance to the Fashion Place mall in Murray in the USA state of Utah, a suburb south of Salt Lake City, said Murray Police Officer Kenny Bass.
The mall said in a tweet it was "very saddened by the incident" and grateful for the actions of security and Murray police.
The shooting happened at the Fashion Place mall in Murray, a spokesperson for the Murray Police Department told ABC News.
"At this time we are directing all inquiries to the Murray Police Department". Nothing is more important than the safety and well-being of our guests and tenants.
A witness said the suspects were wearing dark trousers and light-colored hoodies, ABC4 reported.
Police believe the shooting was possibly gang related.
The deceased were identified as Azeem (18), Waqas (18), Arshad (18), all residents of the district, and Sultan (22), Superintendent of Police (Rural) Sansar Singh said.
"At this point, there are officers still looking for them", Bass told KSL. He said he's never heard of a shooting like this happening in Murray before. Bass said employees and mall patrons would likely be able to return to the mall to retrieve personal items about 4 p.m.
Video posted to social media shows people inside the indoor mall running after multiple gunshots were fired. "Hurry!' People thought it was a fire", she said. She said 10 to 12 employees and around 20 customers hid in the store's upstairs stockroom. "Women and children are getting trampled, especially little kids".
Murray is 6.6 miles (11 kilometers) south of Salt Lake City. Any details about a potential connection between the victims and shooters was not immediately released Sunday.
"We saw cops come in from everywhere", Loren Okuly, who was in the parking lot at the time of the shooting, told KSL.
She added: "Guys running, from like Cheesecake Factory toward Red Rock Brewery with not pistols, but full on assault rifles in their hands".