Assistant Sheriff Kevin McMahill said the two suspects, Jerad Miller and his wife, Amanda, had ideology that was along the lines of "militia and white supremacists" and that law enforcement was the "oppressor."
Police believe the shootings were an isolated act and officers were still looking for a motive, McMahill said.
Ammon Bundy, one of Cliven Bundy's sons, said by telephone that it is possible the Millers were at the ranch, the scene of an armed standoff with federal agents, but that "we have not found anybody that recognizes them." He said thousands of people have come to his father's ranch over the past several months.
The two officers were having lunch Sunday at a pizza buffet in a strip mall when the Millers fatally shot them at point-blank range.
The attack at a CiCi's Pizza killed officers Alyn Beck, 41, and Igor Soldo, 31, who were both husbands and fathers. Jerad Miller yelled, "This is a revolution!" McMahill said.
Both suspects fired multiple shots into Beck. They then placed a note, a yellow "Don't tread on me" flag and a swastika on the officers' bodies, McMahill said at a news conference Monday.
The deadly rampage in the aging shopping center about 5 miles northeast of the Las Vegas Strip unfolded in a matter of minutes.
The suspects then fled on foot to a nearby Wal-Mart, where Jerad Miller fired a single shot upon entering, police said. A patron at the store who carried a firearm confronted Jerad Miller, not realizing that he was accompanied by Amanda Miller, who shot and killed the man, police said. He was identified as 31-year-old Joseph Wilcox of Las Vegas.
"Joseph died trying to protect others," Sheriff Doug Gillespie said.
As terrified customers fled the store, the Millers went to the rear and hunkered down for a firefight with police, McMahill said. Though they exchanged gunfire, ultimately, Amanda Miller shot and killed her husband, and then shot herself, police said.
Police were called at 11:22 a.m. to the pizzeria. Shots were reported five minutes later at the Wal-Mart.
Bundy and his supporters, some of them armed militia members, thwarted a Bureau of Land Management roundup of his cattle near Bunkerville in April. The BLM says Bundy owes more than $1 million in grazing fees and penalties for trespassing without a permit over 20 years, but he refuses to acknowledge federal authority on public lands.
Ammon Bundy said his family "has had no quarrel" with Las Vegas police and disavowed the Millers' actions.
"The only thing worse than tyranny is anarchy, and we certainly recognize that," Bundy said.
The Millers moved to the Las Vegas area in January, police said. Amanda Miller had worked at a Hobby Lobby craft store in Las Vegas, the chain store said in a written statement, but was no longer employed there.
Jerad Miller, 31, was convicted of felony vehicle theft in Washington state, police said. He also had a criminal record in Indiana.
Miller and his 22-year-old wife were married in August 2012, according to a marriage license on file in Indiana.
Associated Press researcher Judith Ausuebel in New York contributed to this report.
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