LAS VEGAS — A husband and wife who went on a deadly shooting rampage in Las Vegas harbored anti-government beliefs and left a swastika and a “Don’t tread on me” flag on the body of one of the two police officers they killed, authorities said Monday.

Jerad and Amanda Miller had been kicked off a Nevada ranch where anti-government protesters faced down federal agents earlier this year because they were “very radical,” according to the son of rancher Cliven Bundy.

Assistant Sheriff Kevin McMahill said the Millers had ideology shared by “militia and white supremacists,” including the belief that law enforcement was the “oppressor.”

Police believe the shootings were an isolated act, not part of a broader conspiracy to target law enforcement, McMahill said.

Ammon Bundy, one of Cliven Bundy’s sons, said by telephone that the Millers were at his father’s ranch for a few days this spring before they were asked to leave by militia members for unspecified “conduct” problems. He called the couple “very radical” and said they “did not align themselves” with the beliefs of other protesters, who thwarted a roundup of Cliven Bundy’s cattle by the U.S. Bureau of Land Management, which wants to collect more than $1 million in grazing fees and penalties.

While thousands of people have been to the site over the last couple of months, “Not very many people were asked to leave. I think they may have been the only ones,” Ammon Bundy said.

On Sunday, the two Las Vegas police officers were having lunch at a pizza buffet in an aging strip mall about 5 miles northeast of the Las Vegas Strip when the Millers fatally shot them. The attack at a CiCi’s Pizza killed officers Alyn Beck, 41, and Igor Soldo, 31, both of whom were husbands and fathers.

According to McMahill, this is how Sunday’s events unfolded:

The Millers left a neighbor’s apartment where they had been staying around 4:30 a.m. and walked for hours, eventually reaching the strip mall, about 5 miles away.

Around 11:20 a.m., Jerad Miller went briefly into the restaurant, then left and got his wife, leaving their backpacks outside.

When they returned, the two officers were sitting in a booth. Jerad Miller fatally shot Soldo in the back of his head. As his partner tried to react, Miller shot him once in the throat. Amanda Miller then pulled her own gun and both shot Beck several times.

Police believe that while the Millers wanted to target police, the choice of Soldo and Beck was random.

Pulling the mortally wounded officers from the booth, they took their guns and ammunition and put a yellow Gadsden flag featuring the phrase “Don’t tread on me” and a swastika on Beck’s body. The flag, with its roots in the American Revolution, is a symbol for anti-government groups. Police said they believe the swastika was intended to paint police as Nazis, not necessarily as an expression of the Millers’ own white-supremacist views.

The couple also told restaurant patrons that their act was “the beginning of the revolution,” the same message as a note they left at the restaurant.

The couple went next to a Wal-Mart about a block away, where Jerad Miller entered, fired one round and “told the people to get out and this was a revolution and that the police were on the way.”

In the frenzy, shopper Joseph Wilcox decided to confront Jerad Miller — not realizing that Amanda Miller was his accomplice. Wilcox went from the checkout area to Miller and pulled his concealed firearm. But before he could fire, Amanda Miller shot him in the ribs and Wilcox collapsed.

“Joseph died trying to protect others,” Sheriff Doug Gillespie said.

By now, police had arrived, and two five-officer teams entered the massive store. Near the back, one team confronted the Millers, and exchanged fire. At one point, Jerad Miller tried to blast a rear emergency exit door open with a shotgun, but police had blocked it with a car and he could not escape.

By looking at the store’s surveillance camera feeds, an officer saw that Jerad Miller had built a makeshift barricade around his wife.

As police closed in, Amanda Miller shot her husband several times with a handgun, killing him. She then shot herself in the head. When officers arrived, she was still breathing, and was taken to the hospital. She later died.

Police found hundreds more rounds of unspent ammunition in the Millers’ bags.

The couple moved to the Las Vegas area in January, police said. Amanda Miller had worked at a Hobby Lobby craft store there until she was fired in April, the chain store said in a written statement.

Jerad Miller, 31, was convicted of felony vehicle theft in Washington state, and several other offenses, including phone harassment, driving under the influence, theft and malicious mischief, between 2001 and 2003, according to a Washington State Patrol database.

He also had a criminal record in Indiana.

Miller attended Kennewick High School in Washington state for one semester in 1999, his freshman year, district spokeswoman Robyn Chastain said. The district had no other record of him attending schools in the district, or of what he did when he left the school.

He and his 22-year-old wife were married in August 2012, according to a marriage license on file in Indiana.

When police descended on their apartment complex Sunday night in a rundown neighborhood, officers evacuated other residents.

On Monday, Sheriff Gillespie said he was pairing officers together for safety and that, for now, 300 will be on patrol — twice what is normal.

Asked about worries that more officers may be targeted, he responded: “Is that weighing? Sure, there’s no doubt about it.”

Ammon Bundy said supporters of his father are saddened by the killings and “have had no quarrel” with Las Vegas police.

“The only thing worse than (government) tyranny is anarchy,” he said. “And we certainly recognize that.”