Police are investigating social media postings in which one of the Las Vegas shooters rants against the government and announces the "dawn of a new day".

Jerad Miller (31), and his wife Amanda Miller (22) also posed as Batman villains the Joker and Harley Quinn in a Facebook photo.

The couple who killed two policemen and a good Samaritan on Sunday shared anti-government and white supremacist ideologies, authorities said.

Officers Alyn Beck and Igor Soldo shot dead

They placed a yellow "Don't Tread On Me" flag and a swastika on the officers' bodies, officials said.

The yellow flag, with its roots in the American Revolution, is a symbol for anti-government groups.

In a YouTube video, Jerad Miller, can be seen saying he is under house arrest for selling pot. The camera then focuses on an ankle bracelet before he rants against what he describes as an authoritarian US government.

Pointing to a courthouse that can be seen from his window, he calls it a "monument to authoritarianism".

He laments citizens must go to the courthouse and "submit, crawling and grovelling on your hands and feet: 'Oh give me permission to do this, give me permission to do that'."

He says: "Sounds a little like Nazi Germany to me, or maybe Communist Russia."

Dressed up as Joker

In another online video, dressed as the Joker, he says he is running for President: "Year after year I’ve watched you Americans, my fellow citizens, vote for tyranny."

In his last Facebook posting, he says: "The dawn of a new day. May all of our coming sacrifices be worth it."

The attack at a CiCi's Pizza restaurant on Sunday killed Officers Alyn Beck (41), and Igor Soldo (31).

Police believe while the Millers wanted to target police, the choice of Mr Soldo and Mr Beck, who were having lunch at the restaurant, was random.

The Millers then fled to a Walmart across the street, where they gunned down Joseph Wilcox (31), who pulled his concealed firearm but was shot by Amanda Miller.

When police arrived at the scene, she shot her husband several times with a handgun, killing him, before shooting herself in the head.

It has also emerged the Millers went to Cliven Bundy's Nevada ranch during a stand-off with federal authorities in April, but they were kicked off because they were "very radical," according to Mr Bundy's son.

Ammon Bundy said the Millers were at his father's ranch for a few days before they were asked to leave by militia members for unspecified "conduct" problems.

He told the AP news agency the couple "did not align themselves" with the beliefs of other protesters.