One of the attackers yelled "This is the start of a revolution" before shooting the officers and stripping them of their weapons and ammunition, the Las Vegas Review-Journal said.
Two officers were "ambushed" and shot by the gunmen -- a man and a woman -- as they ate lunch at CiCi's Pizza, Sheriff Douglas Gillespie told reporters. One of the officers died at the scene, while the second subsequently died in surgery.
A police dispatch call was made around 11:22 am (1822 GMT).
The attackers then ran across the parking lot to a nearby Walmart store, and the Review-Journal said they exchanged gunfire with and ultimately killed a civilian who was carrying a concealed weapon.
The civilian, who has not yet been identified, was found dead inside the front door.
"It's a tragic day, it's a very, very difficult day but we still have a community to police and we still have a community to protect," Gillespie said.
"We will be out there doing it with our heads held high but an emptiness in our hearts."
The male shooter, described as a tall white man, yelled "everyone get out" before shooting, Assistant Sheriff Kevin McMahill told a news conference earlier.
The two gunmen, who have not yet been named, then went to the back of the Walmart for "some kind of suicide pact," McMahill added.
Gillespie said a preliminary investigation suggested the woman had first shot the man before taking her own life.
"What precipitated this event, we do not know," Gillespie said.
"My officers were simply having lunch when the shooting started."
Gillespie named the slain officers as Alyn Beck, 42, and Igor Soldo, 32. He said they both had young families "devastated" by the tragedy.
"We have lost two officers with young families and a family of law enforcement that cares very, very much about them, as well as a community that cares very, very much about them as well as the innocent citizen that lost their life," he said.
Las Vegas police are doubling up their patrols in the wake of the incident.
