A further five people were said to have been wounded in the shooting, at the Westroads Mall in Omaha.
There were reports that the gunman had turned the gun on himself, though this was not confirmed by police.
Police sealed the exits and emergency workers were seen ferrying stretchers into the building.
There have been differing accounts of the incident.
According to one report, the gunman shot people at random from a balcony in the shopping centre.
Others said the shooting appeared to have taken place in the Von Maur department store.
Keith Fidler, a Von Maur employee, said he heard a burst of five to six shots followed by 15 to 20 more shots.
A worker from another shop said customers and employees were huddled in a storeroom.
"All we know was people were running and screaming down the hallway by Von Maur saying there was a shooting, and then [police] locked us down," she said.
Earlier in the day, President George W Bush had been in Omaha for a fundraiser, but he left the city before the shooting occurred.
Published: 2007/12/05 22:27:22 GMT
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